What is (4^{-1}x^{-2})/((4x)^2) ?

The solution to (4^{-1}x^{-2})/((4x)^2) is 1/(64x^4)

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simplify (4^{-1}x^{-2})/((4x)^2)

simplify

\frac{4 ^{- 1} x ^{- 2}}{( 4 x ) ^{2}}

\frac{1}{64 x ^{4}}

Solution steps

\frac{4 ^{- 1} x ^{- 2}}{( 4 x ) ^{2}}

Apply exponent rule:

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

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

= \frac{4 ^{- 1} x ^{- 2}}{4 ^{2} x ^{2}}

\frac{4 ^{- 1}}{4 ^{2}} = \frac{1}{4 ^{3}}

= \frac{x ^{- 2}}{4 ^{3} x ^{2}}

Simplify

\frac{x ^{- 2}}{x ^{2}} : \frac{1}{x ^{4}}

= \frac{1}{4 ^{3} x ^{4}}

4^{3} = 64

= \frac{1}{64 x ^{4}}

50 - 18 + 32

a^{2} b (2 a x - 3 b y - a b^{2})

\frac{72}{3} + 50

64 + 36

\frac{1}{0 - 1}

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