Power of Literal Quantities will help to represent very large numbers or very small numbers in a simplified manner. The Power of Literal Quantities means representing a quantity that is multiplied by itself any number of times. The product with the power is called the power of quantities. If we take the quantity, a^{7}, then the quantity a is multiplied by itself 7 times. Let us check the representation, identification, and also solved examples on powers related to linear quantities.

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## How to Represent Power of Literal Quantities?

The representation of the Power of Literals is clearly given here. The repetition of a literal with the power consists of the base, and its multiplicative power represents the index. Also, in the product, the factors are written slightly raised to the right of the quantity. You can also check the examples along with an explanation here.

**Examples:**

- If we take the expression ‘m’ and multiply itself by 5 times, then it must be m x m x m x m x m = m
^{5} - If we take the expression ‘b’ and multiply itself by 7 times, then it must be b Ã— b Ã— b Ã— b Ã— b Ã— b Ã— b = b
^{7}

### How to Read and Write the Exponents of Literal Quantities?

We will read and write the number formed by any power of literal in the below manner.

- The product of a Ã— a is written as a
^{2}and it is read as a squared or a raised to the power 2. - The product of m Ã— m Ã— m is written as m
^{3}and it is read as a cubed or m raised to the power 3. - And, the product of n Ã— n Ã— n Ã— n Ã— n is written as n
^{5}and it is read as the fifth power of n or n raised to the power 5. - The product of p Ã— p Ã— p Ã— p Ã— p Ã— p Ã— p is written as p
^{7}and it is read as the seventh power of p or p raised to the power 7.

### How to Identify the Base and Exponent of the Power of the Given Quantity?

We will generally represent the power of numbers or the power of quantities with two terms. The number that has power will consist of base and exponent. The repeated multiplication of the same factor or number is represented in the form of the power of an expression. The value of the exponent depends on the number of times the base multiplied by itself.

(i) In y^{3} here y is called the base and 3 is called the exponent or index or power.

(ii) In N^{m} here N is called the base and m is called the exponent or index or power.

Also, See: Convert Exponentials and Logarithms

### Rules of Exponents

The rules of exponents are as follows.

(i) x^{0}Â = 1

If the power of any integer or quantity is zero, then the resulted output will be one or unity.

(ii) (x^{m})^{n} = x(^{mn})

â€˜xâ€™ raised to the power â€˜mâ€™ and then raised to the power â€˜nâ€™ which is equal to â€˜xâ€™ raised to the power product of â€˜mâ€™ and â€˜nâ€™.

(iii) x^{m} Ã— y^{m} =(xy)^{m}

The product of â€˜xâ€™ raised to the power of â€˜mâ€™ and â€˜yâ€™ raised to the power â€˜mâ€™ that is equal to the product of â€˜xâ€™ and â€˜yâ€™ whole raised to the power â€˜mâ€™.

(iv) x^{m}/y^{m} = (x/y)^{m}

The division of â€˜xâ€™ raised to the power â€˜mâ€™ and â€˜yâ€™ raised to the power â€˜mâ€™ that is equal to the division of â€˜xâ€™ by â€˜yâ€™ whole raised to the power â€˜mâ€™.

### Power of Literal Quantities Examples with Solutions

**Question 1.**

Write m Ã— m Ã— n Ã— n Ã— n in index form.

**Solution:
**In this problem, m’s are written 2 times and n’s are written 3 times. So, the problem can be rewritten as an exponent of m

^{2}n

^{3}.

Therefore, the answer is m Ã— m Ã— n Ã— n Ã— n = m^{2}n^{3}.

**Question 2.**

Express 4 Ã— a Ã— a Ã— a Ã— b Ã— b in power form.

**Solution:
**In this problem, a’s are written 3 times and b’s are written 2 times. So, the problem can be rewritten as an exponent of a

^{3}b

^{2}

Therefore, the answer is 4 Ã— a Ã— a Ã— a Ã— b Ã— b = 4a^{3}b^{2}.

**Question 3.**

Express -6 Ã— 2 Ã— r Ã— s Ã— s Ã— p in exponent form.

**Solution:
**In this problem, s’s are written 2 times. So, the problem can be rewritten as an exponent of s

^{2}

Therefore, the answer is -6 Ã— 2 Ã— r Ã— s Ã— s Ã— p = -12prs^{2}.

**Question 4.**

Write 6a^{4}b^{3}Â in product form.

**Solution:
**The given expression is 6a

^{4}b

^{3}.

The power of a is 4. So, a is multiplied itself by 4 times i.e, a Ã— a Ã— a Ã— a.

The power of b is 3. So, b is multiplied itself by 3 times i.e, b Ã— b Ã— b.

Therefore, the answer is 6a^{4}b^{3} = 6 Ã— a Ã— a Ã— a Ã— a Ã— b Ã— b Ã— b.

**Question 5.**

Express 7p^{4}q^{2}r^{3}Â in product form.

**Solution:
**The given expression is 7p

^{4}q

^{2}r

^{3}.

The power of p is 4. So, p is multiplied by itself 4 times i.e, p Ã— p Ã— p Ã— p.

The power of q is 2. So, q is multiplied by itself 2 times i.e, q Ã— q.

Also, the power of r is 2. So, r is multiplied by itself 3 times i.e, r Ã— r Ã— r.

Therefore, the answer is 7p^{4}q^{2}r^{3} = 7 Ã— p Ã— p Ã— p Ã— p Ã— q Ã— q Ã— r Ã— r Ã— r.

### FAQs on Index of Literal Quantities

**1. Identify the Base and Exponent of x ^{n}**

The base of x^{n }is x and the exponent is n.

**2. If the base is 4 and the exponent is 5, then write its product.**

If the base is 4 and the exponent is 5, then its product is 4^{5}.

**3. What is the Power of Literal Quantities?**

The Power of literal quantities is defined as a quantity multiplied by itself and the product with power is called the power of literal quantity.

**4. What do we call m ^{2}**

We read m^{2 }as m squared or m raised to power 2.

### Conclusion

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