# MULTIPLICATION WITH EXPONENTS

## About "Multiplication with exponents"

Multiplication with exponents :

To simplify two or more exponent terms expressed in multiplication with same bases, we have to write the base once and add the powers. Let us see some example problems based on the above concept.

Example 1 :

Find the value of the following

3⁴ x 3³

Solution :

Since we have same bases for both terms, we have to write the base once and add the powers.

3⁴ x 3³  =  3^(-4-3)

=  3^(-7)

In order to change the power as positive, we have to write the reciprocal form.

=  1/3

Example 2 :

Find the value of the following

(2/8)^2 x   (2/8)^x  =  (2/8)^6

Solution :

Since we have same bases for both terms on the left side, we have to combine them

(2/8)^(2 x + x)  =  (2/8)^6

(2/8)^(3 x)  =  (2/8)^6

Since we have same bases on either sides of equal signs, we have to equate the powers

3x  =  6

Divide 3 on both sides,

3x/3  =  6/3

x  =  2

Example 3 :

Find the value of the following

(-2) x (-2)^6

Solution :

Since we have same bases for both terms, we have to write the base once and add the powers.

(-2) x (-2)^6  =  (-2)^(- 5 + 6)

=  (-2)^1

=  -2

Hence the answer is -2.

Example 4 :

Find the value of the following

(-4) x (-4)

Solution :

Since we have same bases for both terms, we have to write the base once and add the powers.

(-4) x (-4)  =  (-4)^(5 + 8)

=  (-4)^13

Hence the answer is (-4)^13.

Example 5 :

Find the value of the following

(-3)  (5/3)

Solution :

First we have to distribute the power 4 for both numerator and denominator.

(-3)  (5/3)⁴  =  (-3)⁴   (5⁴ / 3⁴)

Since we have even power, the base will become positive.

=  (3)⁴   (5⁴ / 3⁴)

=  5⁴

=   625

Hence the answer is 625.

Example 6 :

Find the value of the following

(4P)³ (2P)²   P

Solution :

First we have to distribute the powers 3 and 2.

(4P)³ (2P)²   P   =  4³ ⋅ p³ ⋅ 2² ⋅ P² P

=  4³ ⋅  p³ P²⋅ P⁴

=  64 ⋅ 4 p^(3 + 2 + 4)

=  256 p^9

Hence the answer is 256 p^9. After having gone through the stuff given above, we hope that the students would have understood "Multiplication with exponents".

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