# EXPONENT PROPERTIES WITH PARENTHESES

There are two important rules in the topic  "Exponent properties with parentheses". Those are

(i) Whenever we have exponent raised by another exponent, we have to multiply those exponents.

(ii) Whenever we have common power for two or more numbers or variables which are multiplied inside the parenthesis. We have to distribute the power for those terms which are multiplied

Note:

This rule is not applicable for addition and subtraction of two terms.

For example (x + y) ^m = (x^m + y^m) is not correct

Other things:

Point 1:

If we don't have any number in the power then we have to consider that there is 1

## Negative numbers with fractions

Point 2:

In case we have negative power for any fraction and we want to make it as positive, we can write the power as positive and we should write its reciprocal only. For example

now we have to distribute the power for both numerator and denominator. So, we will get 3²/5² =9/25

## Negative numbers with negative exponents

Find the value of (-5) ³

To find the value of the above expression, first we have to consider the power.

• If the power is odd, then the answer will have negative sign.
• If the power is even, then the answer will have positive sign.

here, the power of -5 is 3, that is odd. So, the answer will have negative sign and we have to multiply the base three times.

Finally we will get -125 as the answer.

Procedure of multiplying two terms with exponents

Whenever we want to multiply two or more terms, we have to follow the below order.

(1) Symbol

(2) Number

(3) Variable

Let us see how it works

Multiply ( 5 x² ) and (-2 x³)

=  ( 5 x² )  x (-2 x³)

=  10 x

## Example problems of exponent properties with parentheses

Question 1 :

Simplify (5x²)⁴ x (2x)³

Solution :

=  (5x²)⁴ x (2x)³

5⁴ = 5 x 5 x 5 x 5

2³ = 2 x 2 x 2

Since x⁸ and x³ are having same base, we can combine these terms.

Let us see the next example on "Exponent properties with parentheses"

 Question 2 :Find the value of 2(256) ^(-1/8)Solution :             = 2 (2^8)^(-1/8)             = 2 (2^-1)             = 2/2             = 1

Let us see the next example on "Exponent properties with parentheses"

Question 3 :

Find the value of (81 x⁴/y⁸)^1/4

Solution :

Let us see the next example on "Exponent properties with parentheses"

Question 4 :

Find the value of (8/27)^(-1/3) (32/243)^(-1/5)

Solution :

## More about basic laws of exponents

Basic laws of exponents:

## Multiplying same base with different exponents

When we have to simplify two or more terms which are multiplying with same base,then we have to put the same base and add the powers.

## Dividing same base with different exponents

Whenever we have two terms which are diving with the same base,we have to put only one base and we have to subtract the powers.

## Any number to the power zero

How to move an exponents or powers to the other side ?

 If the power goes from one side of equal sign to the other side,it will flip.that is x = 4²

More example problems using laws of exponents:

Example 1 :

Simplify 4 x ^(-1)/x^(-1/3)

Solution :

Example 2 :

Find the value of x^(a - b) x^(b - c) x^(c - a)

Solution :

After having gone through the stuff given above, we hope that the students would have understood "Let us see the next example on "Exponent properties with parentheses"

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