**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.

(1) Find the value of the following

3⁻⁴ x 3⁻³

(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)⁻⁵ x (-2)^6

(4) Find the value of the following

(-4)⁵ x (-4)⁸

(5) Find the value of the following

(-3)⁴ ⋅ (5/3)⁴

(6) Find the value of the following

(4P)³⋅ (2P)² ⋅ P⁴

**Question 1 :**

Find the value of the following

3⁻⁴ x 3⁻³

**Solution : **

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

3⁻⁴ x 3⁻³ = 3^(-4-3)

= 3^(-7)

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

= 1/3⁷

**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)⁻⁵ x (-2)^6

**Solution : **

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

(-2)⁻⁵ x (-2)^6 = (-2)^(- 5 + 6)

= (-2)^1

= -2

Hence the answer is -2.

**Question 4 :**

Find the value of the following

(-4)⁵ x (-4)⁸

**Solution : **

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

(-4)⁵ x (-4)⁸ = (-4)^(5 + 8)

= (-4)^13

Hence the answer is (-4)^13.

**Question 5 :**

Find the value of the following

(-3)⁴ ⋅ (5/3)⁴

**Solution : **

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

(-3)⁴ ⋅ (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.

**Question 6 :**

Find the value of the following

(4P)³⋅ (2P)² ⋅ P⁴

**Solution : **

First we have to distribute the powers 3 and 2.

(4P)³⋅ (2P)² ⋅ P⁴ = 4³ ⋅ p³ ⋅ 2² ⋅ P²⋅ P⁴

= 4³ ⋅ 2²⋅ 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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