McGraw Hill My Math Grade 5 Chapter 2 Lesson 3 Answer Key Powers and Exponents

iAll the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 2 Lesson 3 Powers and Exponents will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 2 Lesson 3 Powers and Exponents

Math in My World

Example 1
The number of Calories in six pancakes can be written as 10³. Write 10³ as a product of the same factor. Then find the value.

10 × 10 × 10 = ____
Six pancakes have ____ Calories.
Answer:
1000
Six pancakes have 1000 Calories.

Explanation:
Given,
10 × 10 × 10 = 1000 = 10³
Six pancakes have 1000 Calories.

Example 2
Write 3 × 3 × 3 × 3 using an exponent.
The base is _______. Since 3 is used as a factor ____ times, the exponent is ___.
Write as a power. 3 × 3 × 3 × 3 = ____
Answer:
The base is 3. Since 3 is used as a factor 4 times, the exponent is 4.
3 × 3 × 3 × 3 = 81

Example 3.
Write the prime factorization of 72 using exponents.
Answer:
2³ × 3²

Explanation:
Given,
72
8 × 9
4 × 2 × 9
2 × 2 × 2 × 3 × 3
2³ × 3²

Question 1.
Complete the factor tree.

Answer:

Question 2.
Order the factors from least to greatest.
___ × ___ × ____ × ____ × ___
Answer:
2 × 2 × 2 × 3 × 3

Explanation:
The factors from least to greatest is 2 × 2 × 2 × 3 × 3.

Question 3.
Write products of identical factors using exponents.

So, 72 = ____ × ____
Answer:

72
8 × 9
4 × 2 × 9
2 × 2 × 2 × 3 × 3
2³ × 3²

Talk Math
Explain how a factor tree helps you to write the prime factorization of a number using exponents.

Guided Practice

Question 1.
Write 4 × 4 × 4 × 4 using an exponent.
The base is ___. Since 4 is used as a factor times, the exponent is
4 × 4 × 4 × 4 = ___
Answer:
The base is 4. Since 4 is used as a factor times, the exponent is 4.
4 × 4 × 4 × 4 = 256

Independent Practice

Write each product using an exponent.

Question 2.
10 × 10 = ___
Answer:
10²

Explanation:
The each product using an exponent is 10²

Question 3.
8 × 8 × 8 × 8 = ___
Answer:
8⁴

Explanation:
The each product using an exponent is 8⁴

Question 4.
3 × 3 × 3 × 3 × 3 × 3 = ___
Answer:
3⁶

Explanation:
The each product using an exponent is 3⁶

Question 5.
5 × 5 × 5 × 5 × 5 = ____
Answer:
5⁵

Explanation:
The each product using an exponent is 5⁵

Question 6.
9 × 9 × 9 × 9 = ___
Answer:
9⁴

Explanation:
Each product using an exponent is 9⁴

Question 7.
1 × 1 × 1 × 1 × 1 = ____
Answer:
1⁵

Explanation:
Each product using an exponent is 1⁵

Write each power as a product of the same factor. Then find the value.

Question 8.
10⁴ = ____
Answer:
10000

Explanation:
Given,
10⁴
10 × 10 × 10 × 10
10000

Question 9.
3² = ____
Answer:
9

Explanation:
Given,
3²
3 × 3 = 9

Question 10.
9³ = ____
Answer:
729

Explanation:
Given,
9 × 9 × 9
729

Question 11.
6⁵ = ____
Answer:
7776

Explanation:
Given,
6⁵
6 × 6 × 6 × 6 × 6 × 6
7776

Write the prime factorization of each number using exponents.

Question 12.
25 = ___
Answer:
5 × 2²

Question 13.
56 = ____
Answer:
2³  × 7

Explanation:
8 × 7
2 × 2 × 2 × 7
2³  × 7

Question 14.
68 = ___
Answer:
17 × 2 × 2
17 × 2²

Question 15.
88 = ___
Answer:
11 × 2³

Explanation:
Given,
88 =
11 × 8
11 × 2 × 2 × 2
11 × 2³

Problem Solving

Question 16.
To find the amount of space a cube-shaped bird cage occupies, find the cube of the measure of one edge of the bird cage. Express the amount of space occupied by the bird cage shown as a power. Then find the amount in cubic units.

Answer:
5832 units.

Explanation:
To find the amount of space a cube-shaped bird cage occupies, we need to find the volume of the page. Mutiply the edge length (18 units) by itself three times.
Volume = 18 × 18 × 18
= 5832 units
18³

Question 17.
A single tusk that weighed just over 2 pounds from an African elephant is the largest tooth ever recorded from any modem animal. About how many pounds did the tusk weigh?
Answer:

Hot Problems

Question 18.
Mathematical PRACTICE 2 Reason Which is greater: 3⁵ or 5³? Explain your reasoning.
Answer:
3⁵ = 243 and  5³ = 125
3⁵ is greater than the number 5³

Question 19.
? Building on the Essential Question What does it mean for a product of factors to be expressed using exponents?
Answer:
A product factor is called an expression in which you multiply the same value digit many times.
Exponent is the expression where you can convert product factor expression into a shorter expression.
Example:
The product factor
8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 = 10⁹
8 is multiplied many times the exponent expression is where 8 is the base and 9 is called the exponent.

McGraw Hill My Math Grade 5 Chapter 2 Lesson 3 My Homework Answer Key

Practice

Write each product using an exponent.

Question 1.
10 × 10 × 10 = ____
Answer:
10³

Explanation:
Given,
10 × 10 × 10
1000
10³

Question 2.
12 × 12 = ____
Answer:
12²

Explanation:
Given,
12 × 12
144
12²

Write each power as a product of the same factor. Then find the value.

Question 3.
3⁷ = _________
Answer:
2187

Explanation:
Given
3⁷
3 × 3 × 3 × 3 × 3 × 3 × 3
2187

Question 4.
10⁶ = ____
Answer:
1000000

Explanation:
Given,
10⁶
10 × 10 × 10 × 10 × 10 × 10
100000

Write the prime factorization of each number using exponents.

Question 5.
20 = ____
Answer:
5 × 4

Explanation:
The prime factorization of each number using exponents is
5 × 2²

Question 6.
50 = ____
Answer:
25 × 2
5² × 2

Explanation:
The prime factorization of each number using exponents is 5² × 2 .

Problem Solving

Question 7.
Mathematical PRACTICE 8 Look for a Pattern The Newfoundland is a large breed of dog. It weighs
about 10 × 10 pounds. Write 10 × 10 using an exponent. Then find the value of the power. How many pounds does the Newfoundland weigh?

Answer:
100 pounds.

Explanation:
10 × 10 = 10²
power = 2
100 pounds

Question 8.
The area of San Bernardino County, California, the largest county in the United States, is about
3⁹ square miles. Write this as an expression. What is the area of San Bernardino County?
Answer:
3⁹ square miles
19683 square miles

Explanation:
We are given that the area of San Bernardino County, California, the largest county in the United States, is about
3⁹ square miles
3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3
19683
The area of San Bernardino County is 19683 Square miles.

‘Vocabulary Check

Fill in each blank with the correct term or number to complete each sentence.

Question 9.
Numbers expressed using exponents are called _______
Answer:
powers.

Explanation:
Numbers expressed using exponents are called powers.

Question 10.
The exponent indicates how many times the ____ is used as a factor.
Answer:
The base

Explanation:
The exponent indicates how many times the base is used as a factor.
a^b
where a = base of the expression
b = exponent of the expression
For example for a = 3 and b = 2
a^b
3² = 3 × 3

Test Practice

Question 11.
A 100-pound person on Earth would weigh about 4 × 4 × 4 × 4 pounds on Jupiter. Evaluate the expression to determine how much a 100-pound person would weigh on Jupiter.
A. 16 pounds
B. 64 pounds
C. 256 pounds
D. 1,024 pounds
Answer:
256 pounds

Explanation:
A 100-pound person on Earth would weigh about 4 × 4 × 4 × 4 pounds
4 × 4 = 16
16 × 4 = 64
64 × 4 = 256 pounds.