Go through the **Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.1 Using Exponents** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 5 Lesson 5.1 Using Exponents Answers Key

A power of a number represents repeated multiplication of the number by itself.

10^{3} = 10 × 10 × 10 and is read 10 to the third power.

In exponential numbers, the base is the number that is multiplied, and the exponent represents the number of times the base is used as a factor. In 2^{5}, 2 is the base and 5 is the exponent.

2^{5} means 2 is used as a factor 5 times.

2 × 2 × 2 × 2 × 2 = 32 2^{5} = 32

Scientific notation for a number is expressed by writing the number as the product of a number between one and ten, and a power of ten.

3,000 can be written as 3 × 1,000 or 3 × 10^{3}.

3 × 10^{3} is scientific notation for 3,000.

Some powers of 10 are shown in the table at right.

**Use the table above to write each number in scientific notation.**

Question 1.

a. 30 ______

Answer:

The given number in Scientific notation can be written as 3 x 10^{1}

b. 4,000 ______

Answer:

The given number in Scientific notation can be written as 4 x 10^{3}

c. 50,000 _____

Answer:

The given number in Scientific notation can be written as 5 x 10^{4}

Question 2.

a. 600,000 ____

Answer:

The given number in Scientific notation can be written as 6 x 10^{5}

b. 700 ____

Answer:

The given number in Scientific notation can be written as 7 x 10^{2}

c. 90 _____

Answer:

The given number in Scientific notation can be written as 9 x 10^{1}

Question 3.

a. 40,000 ____

Answer:

The given number in Scientific notation can be written as 4 x 10^{4}

b. 100,000 ____

Answer:

The given number in Scientific notation can be written as 1 x 10^{5}

c. 400 ____

Answer:

The given number in Scientific notation can be written as 4 x 10^{2}

**Write each power as the product of factors.**

Question 4.

a. 3^{3} ______

Answer:

Given value is 3^{3}

It can be written as a product of 3 x 3 x 3

= 27

Therefore the value of 3^{3 }is 27.

b. 5^{5} ______

Answer:

Given value is 5^{5}

It can be written as a product of 5 x 5 x 5

=125

Therefore the value of 5^{5}^{ }is 125 .

c. 1^{6} ______

Answer:

Given value is 1^{6}

It can be written as a product of 1 x 1 x 1 x 1 x 1 x 1

=1

Therefore the value of 1^{6} ^{ }is 1.

Question 5.

a. 12^{2} ______

Answer:

Given value is 12^{2}

It can be written as a product of 12 x 12

=144

Therefore the value of 12^{2} is 144.

b. 8^{3} ______

Answer:

Given value is 8^{3}

It can be written as a product of 8 x 8 x 8

=512

Therefore the value of 8^{3 } is 512 .

c. 6^{3} ______

Answer:

Given value is 6^{3}

It can be written as a product of 6 x 6 x 6

=216

Therefore the value of 6^{3 } is 216 .

Question 6.

a. 7^{4} ______

Answer:

Given value is 7^{4}

It can be written as a product of 7 x 7 x 7 x 7

=2401

Therefore the value of 7^{4} is 2401.

b. 4^{4} ______

Answer:

Given value is 4^{4}

It can be written as a product of 4 x 4 x 4 x 4

= 256

Therefore the value of 4^{4} is 256 .

c. 11^{4} ______

Answer:

Given value is 11^{4}

It can be written as a product of 11 x 11 x 11 x 11

= 14641

Therefore the value of 11^{4} is 14641.

**Use exponents to rewrite each expression.**

Question 7.

a. 3 × 3 × 3 ____

Answer:

Given 3 x 3 x 3

It can be written as a 3^{3
}= 27

Therefore the value of 3 x 3 x 3 is 3^{3} which is equal to 27.

b. 8 × 8 _____

Answer:

Given 8 x 8

It can be written as 8^{2
}= 64

Therefore the value of 8x 8 is 8^{2} which is equal to 64.

c. 7 × 7 × 7 × 7 × 7 _____

Answer:

Given 7 × 7 × 7 × 7 × 7

It can be written as 7^{5
}= 16,807

Therefore the value of 7 × 7 × 7 × 7 × 7 is 7^{5} which is equal to 16,807.

Question 8.

a. 24 × 24 _____

Answer:

Given 24 × 24

It can be written as 24^{2
}= 576

Therefore the value of 24 × 24 is 24^{2} which is equal to 576.

b. 4 × 4 × 4 _____

Answer:

Given 4 × 4 x 4

It can be written as 4 ^{3
}= 64

Therefore the value of 24 × 24 is 4 ^{3} which is equal to 64.

c. 6 × 6 × 6 × 6 × 6 × 6 _____

Answer:

Given 6 × 6 × 6 × 6 × 6 × 6

It can be written as 6^{6
}=46,656

Therefore the value of 6 × 6 × 6 × 6 × 6 × 6 is 6^{6} which is equal to 46,656 .

Question 9.

a. 2 × 2 × 2 × 2 ____

Answer:

Given 2 × 2 × 2 × 2

It can be written as 2^{4
}= 16

Therefore the value of 2 × 2 × 2 × 2 is 2^{4} which is equal to 16.

b. 38 × 38 × 38 _____

Answer:

Given 38 × 38 × 38

It can be written as 38^{3
}= 54,872

Therefore the value of 38 x 38 x38 is 38^{3 }which is equal to 54,872.

c. 5 × 5 × 5 × 5 × 5 _____

Answer:

Given 5 × 5 × 5 × 5 × 5

It can be written as 5^{5
}= 3125

Therefore the value of 5 x 5 x 5 x 5 x 5 is 5^{5} which is equal to 3125.

Question 10.

a. a^{4} if a = 2 ____

Answer:

Given Expression a^{4}

By Substituting the given value a = 2, the Expression becomes as shown Below

a^{4 }= 1^{4
}= 1 x 1 x 1 x 1

= 1

Therefore the value of a = 1

b. x^{3} if x = 4 ____

Answer:

Given Expression x^{3}

By Substituting the given value x = 4, the Expression becomes as shown Below

x^{3 }= 4^{3
}= 4 x 4 x 4

= 64

Therefore the value of x is 64

c. n^{7} if n = 1 ____

Answer:

Given Expression n^{7}

By Substituting the given value n = 1, the Expression becomes as shown Below

n^{7} = 1^{7}

= 1 x 1 x1 x 1 x 1 x 1 x 1

= 1

Therefore the value of n is 1.

Question 11.

a. n^{2} if n = 8 ____

Answer:

Given Expression n^{2}

By Substituting the given value n =81, the Expression becomes as shown Below

n^{2 }= 8^{2}

= 8 x 8

= 64

Therefore the value of n is 64.

b. b^{4} if b = 3 ____

Answer:

Given Expression b^{4}

By Substituting the given value n =81, the Expression becomes as shown Below

^{b4 }= 3^{4}

= 3 x 3 x 3 x 3

= 81

Therefore the value of b is 81.

c. x^{3} if x = 5 _____

Answer:

Given Expression x^{3}

By Substituting the given value x =5, the Expression becomes as shown Below

^{x3 }= 5^{3}

= 5 x 5 x 5

= 125

Therefore the value of x is 125.

Question 12.

a. a^{5} if a = 3 ____

Answer:

Given Expression a ^{5}

By Substituting the given value a =3, the Expression becomes as shown Below

a ^{5 }= 3^{5}

= 3 x 3 x 3 x 3 x 3

= 243

Therefore the value of a is 243.

b. x^{3} if x = 6 ____

Answer:

Given Expression x^{3}

By Substituting the given value x = 6, the Expression becomes as shown Below

x ^{3} = 6^{3}

= 6 x 6 x 6

= 216

Therefore the value of x is 216.

c. n^{2} if n = 11 ____

Answer:

Given Expression n^{2}

By Substituting the given value n = 11 , the Expression becomes as shown Below

n^{2} = 11^{2}

= 11 x 11

= 121

Therefore the value of n is 121.

**Write each power as the product of factors.**

Question 1.

a.

3^{5} __________

Answer:

Given value is 3^{5}

It can be written as a product of 3 x 3 x 3 x 3 x 3

=243

Therefore the value of 3^{5} is 243 .

b.

9^{3} __________

Answer:

Given value is 9^{3}

It can be written as a product of 9 x 9 x 9

= 729

Therefore the value of 9^{3} is 729.

c.

2^{7} __________

Answer:

Given value is 2^{7}

It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2

=128

Therefore the value of 2^{7} is 128 .

Question 2.

a.

10^{2} __________

Answer:

Given value is 10^{2}

It can be written as a product of 10 x 10

=100

Therefore the value of 10^{2} is 100 .

b.

3^{4} __________

Answer:

Given value is 3^{4}

It can be written as a product of 3 x 3 x 3 x 3

= 81

Therefore the value of 3^{4} is 81.

c.

2^{8} __________

Answer:

Given value is 2^{8}

It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 256

Therefore the value of 2^{8} is 256.

Question 3.

a.

7^{3} __________

Answer:

Given value is 7^{3}

It can be written as a product of 7 x 7 x 7

= 343

Therefore the value of 7^{3} is 343 .

b.

4^{2} __________

Answer:

Given value is 4^{2}

It can be written as a product of 4 x 4

= 16

Therefore the value of 4^{2} is 16 .

c.

7^{2} __________

Answer:

Given value is 7^{2}

It can be written as a product of 7 x 7

= 49

Therefore the value of 7^{2} is 49.

Question 4.

a.

9^{3} __________

Answer:

Given value is 9^{3}

It can be written as a product of 9 x 9 x 9

= 729

Therefore the value of 9^{3} is 729.

b.

8^{1} __________

Answer:

Given value is 8^{1}

It can be written as a product of 8

= 8

Therefore the value of 8^{1} is 8.

c.

12^{2} __________

Answer:

Given value is 12^{2}

It can be written as a product of 12 x 12

= 144

Therefore the value of 12^{2 } is 144.

Question 5.

a.

5^{4} __________

Answer:

Given value is 5^{4}

It can be written as a product of 5 x 5 x 5 x 5

= 625

Therefore the value of 5^{4} is 625.

b.

11^{3} __________

Answer:

Given value is 11^{3}

It can be written as a product of 11 x 11 x 11

= 1331

Therefore the value of 11^{3} is 1331.

c.

6^{5} __________

Answer:

Given value is 6^{5}

It can be written as a product of 6 x 6 x 6 x 6 x 6

= 7,776

Therefore the value of 6^{5} is 7,776.

Question 6.

a.

4^{4} __________

Answer:

Given value is 4^{4}

It can be written as a product of 4 x 4 x 4 x 4

= 256

Therefore the value of 4^{4} is 256.

b.

10^{3} __________

Answer:

Given value is 10^{3}

It can be written as a product of 10 x 10 x 10

= 1000

Therefore the value of 10^{3} is 1000.

c.

8^{6} __________

Answer:

Given value is 8^{6}

It can be written as a product of 8 x 8 x 8 x 8 x 8 x 8

= 2, 62,1 44

Therefore the value of 8^{6} is 2,62,144.

**Use exponents to rewrite each expression.**

Question 7.

a. 3 × 3 × 3 = ____

Answer:

Given Expression 3 × 3 × 3

It can be written as 3^{3}

= 81

Therefore the value of 3 × 3 × 3 is 3^{3} which is equal to 81.

b. 5 × 5 × 5 × 5 × 5 = ____

Answer:

Given Expression 5 × 5 × 5 × 5 × 5

It can be written as 5^{5}

=3125

Therefore the value of 5 × 5 × 5 × 5 × 5 is 5^{5 } which is equal to 3125.

c. 2 × 2 × 2 × 2 × 2 × 2 = _____

Answer:

Given Expression 2 × 2 × 2 × 2 × 2 × 2

It can be written as 2^{6}

= 64

Therefore the value of 2 × 2 × 2 × 2 × 2 × 2 is 2^{6} which is equal to 64.

Question 8.

a. 9 × 9 × 9 = ____

Answer:

Given Expression 9 × 9 × 9

It can be written as 9^{3}

= 729

Therefore the value of 9 × 9 × 9 is 9^{3} which is equal to 729.

b. 4 × 4 × 4 × 4 × 4 × 4 × 4 = ____

Answer:

Given Expression 4 × 4 × 4 × 4 × 4 × 4 × 4

It can be written as 4^{7}

=16384

Therefore the value of 4 × 4 × 4 × 4 × 4 × 4 × 4 is 4^{7} which is equal to 16384.

c. 21 × 21 = ____

Answer:

Given Expression 21 x 21

It can be written as 21^{2}

= 441

Therefore the value of 21 x 21 is 21^{2} which is equal to 441.

Question 9.

a. 10 × 10 × 10 × 10 = ____

Answer:

Given Expression 10 x 10 x 10 x 10

It can be written as 10^{4}

= 10,000

Therefore the value of 10 x 10 x 10 x 10 is 10^{4} which is equal to 10,000.

b. 8 × 8 × 8 × 8 × 8 = ____

Answer:

Given Expression 8 × 8 × 8 × 8 × 8

It can be written as 8^{5}

= 32,768

Therefore the value of 8 × 8 × 8 × 8 × 8 is 8^{5} which is equal to 32,768.

c. 7 × 7 × 7 × 7 = ____

Answer:

Given Expression 7 × 7 × 7 × 7

It can be written as 7^{4}

= 2,401

Therefore the value of 7 × 7 × 7 × 7 is 7^{4} which is equal to 2401.

**Evaluate each expression.**

Question 10.

a. 8^{5} _____

Answer:

Given value is 8^{5}

It can be written as a product of 8 x 8 x 8 x 8 x 8

= 32,768

Therefore the value of 8^{5} is Equal to 32,768.

b. 2^{8} _____

Answer:

Given value is 2^{8}

It can be written as a product of 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 256

Therefore the value of 2^{8} is Equal to 256.

c. 3^{4} _____

Answer:

Given value is 3^{4}

It can be written as a product of 3 x 3 x 3 x 3

= 81

Therefore the value of 3^{4} is Equal to 81.

Question 11.

a. 6^{2} _____

Answer:

Given value is 6^{2}

It can be written as a product of 6 x 6

= 36

Therefore the value of 6^{2} is Equal to 36.

b. 9^{1} _____

Answer:

Given value is 9^{1}

It can be written as a product of 9

= 9

Therefore the value of 9^{1} is Equal to 9.

c. 10^{4} _____

Answer:

Given value is 10^{4}

It can be written as a product of 10 x 10 x 10 x 10

= 10, 000

Therefore the value of 10^{4 } is Equal to 10,000.

Question 12.

a. 4^{4} _____

Answer:

Given value is 4^{4}

It can be written as a product of 4 x 4 x 4 x 4

= 256

Therefore the value of 4^{4 } is Equal to 256.

b. 7^{4} _____

Answer:

Given value is 7^{4}

It can be written as a product of 7 x 7 x 7 x 7

= 2401

Therefore the value of 7^{4 } is Equal to 2401.

c. 12^{2} _____

Answer:

Given value is 12^{2}

It can be written as a product of 12 x 12

= 144

Therefore the value of 12^{2} is Equal to 144 .