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Popular >

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

Solution

simplify

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

Solution

\frac{81}{w ^{8}}

Solution steps

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

Apply exponent rule:

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

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

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

3^{4} = 81

= 81 (w^{- 2})^{4}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

= 81 w^{- 2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= 81 w^{- 8}

Apply exponent rule:

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

w^{- 8} = \frac{1}{w ^{8}}

= 81 \cdot \frac{1}{w ^{8}}

Simplify

81 \cdot \frac{1}{w ^{8}} : \frac{81}{w ^{8}}

= \frac{81}{w ^{8}}

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Frequently Asked Questions (FAQ)

What is (3w^{-2})^4 ?
The solution to (3w^{-2})^4 is (81)/(w^8)