# MULTIPLICATION WITH EXPONENTS WORKSHEET

## About "Multiplication with exponents worksheet"

Multiplication with exponents worksheet :

To simplify two or more exponent terms expressed in multiplication with same bases, we have to write the base once and add the powers.

## Multiplication with exponents worksheet - Practice questions

(1)  Find the value of the following

3⁴ x 3³

(2)  Find the value of the following

(2/8)^2 x   (2/8)^x  =  (2/8)^6

(3)  Find the value of the following

(-2) x (-2)^6

(4)  Find the value of the following

(-4) x (-4)

(5)  Find the value of the following

(-3)  (5/3)

(6)  Find the value of the following

(4P)³ (2P)²   P

## Multiplication with exponents worksheet - Solution

Question 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

Question 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

Question 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

Question 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

Question 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

Question 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 worksheet".

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