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Popular >

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

Solution

simplify

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

Solution

\frac{9}{x ^{8}}

Solution steps

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

Apply exponent rule:

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

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

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

3^{2} = 9

= 9 (x^{- 4})^{2}

Apply exponent rule:

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

assuming

a \geq 0

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

= 9 x^{- 4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= 9 x^{- 8}

Apply exponent rule:

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

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

= 9 \cdot \frac{1}{x ^{8}}

Simplify

9 \cdot \frac{1}{x ^{8}} : \frac{9}{x ^{8}}

= \frac{9}{x ^{8}}

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Frequently Asked Questions (FAQ)

What is (3x^{-4})^2 ?
The solution to (3x^{-4})^2 is 9/(x^8)