What is (((4x^{-2})^{-2})/((4x)^3))^3 ?

The solution to (((4x^{-2})^{-2})/((4x)^3))^3 is (x^3)/(1073741824)

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

simplify

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

\frac{x ^{3}}{1073741824}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

Simplify

((4 x^{- 2})^{- 2})^{3} : \frac{x ^{12}}{4096}

= \frac{\frac{x ^{12}}{4096}}{( ( 4 x ) ^{3} ) ^{3}}

Simplify

((4 x)^{3})^{3} : 262144 x^{9}

= \frac{\frac{x ^{12}}{4096}}{262144 x ^{9}}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{x ^{12}}{4096 \cdot 262144 x ^{9}}

Multiply the numbers:

4096 \cdot 262144 = 1073741824

= \frac{x ^{12}}{1073741824 x ^{9}}

Apply exponent rule:

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

\frac{x ^{12}}{x ^{9}} = x^{12 - 9}

= \frac{x ^{12 - 9}}{1073741824}

Subtract the numbers:

12 - 9 = 3

= \frac{x ^{3}}{1073741824}

18 a + 36

\frac{3}{2} (x - \frac{4}{5}) = - \frac{87}{10}

4 x - 12

3 (u - 2) - 4 u = 2 (u - 9)

6 n^{2} - 19 n - 11

What is (((4x^{-2})^{-2})/((4x)^3))^3 ?
The solution to (((4x^{-2})^{-2})/((4x)^3))^3 is (x^3)/(1073741824)