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Popular >

simplify (2^3)^4*(2^3)^{-5}

Solution

simplify

(2^{3})^{4} \cdot (2^{3})^{- 5}

Solution

\frac{1}{8}

+1

Solution steps

(2^{3})^{4} (2^{3})^{- 5}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(2^{3})^{4} (2^{3})^{- 5} = (2^{3})^{4 - 5}

= (2^{3})^{4 - 5}

Subtract the numbers:

4 - 5 = - 1

= (2^{3})^{- 1}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 2^{3 (- 1)}

3 (- 1) = - 3

= 2^{- 3}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

2^{- 3} = \frac{1}{2 ^{3}}

= \frac{1}{2 ^{3}}

2^{3} = 8

= \frac{1}{8}

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Frequently Asked Questions (FAQ)

What is (2^3)^4*(2^3)^{-5} ?
The solution to (2^3)^4*(2^3)^{-5} is 1/8