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Popular >

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

Solution

simplify

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

Solution

\frac{1}{64}

+1

Decimal Notation

0.015625

Solution steps

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

(4^{- 3})^{3} = \frac{1}{262144}

= \frac{1}{262144} (4^{2})^{3}

Apply exponent rule:

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

(4^{2})^{3} = 4^{2 \cdot 3}

= \frac{1}{262144} \cdot 4^{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{1}{262144} \cdot 4^{6}

4^{6} = 4096

= \frac{1}{262144} \cdot 4096

\frac{1}{262144} \cdot 4096 = \frac{1}{64}

= \frac{1}{64}

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Frequently Asked Questions (FAQ)

What is (4^{-3}*4^2)^3 ?
The solution to (4^{-3}*4^2)^3 is 1/64