What is (1/2)^2 1/((-1/4)^3)(2/3)^2 ?

The solution to (1/2)^2 1/((-1/4)^3)(2/3)^2 is -64/9

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simplify (1/2)^2 1/((-1/4)^3)(2/3)^2

simplify

(\frac{1}{2})^{2} \frac{1}{( - \frac{1}{4} ) ^{3}} (\frac{2}{3})^{2}

- \frac{64}{9}

Decimal Notation

- 7.11111 \dots

Solution steps

(\frac{1}{2})^{2} \frac{1}{( - \frac{1}{4} ) ^{3}} (\frac{2}{3})^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

(\frac{1}{2})^{2} (\frac{2}{3})^{2} = (\frac{1}{2} \cdot \frac{2}{3})^{2}

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

Cross-cancel:

2

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

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

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

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

1 \cdot 4^{3} = 4^{3}

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

4^{3} = 64

= - \frac{64}{3 ^{2}}

3^{2} = 9

= - \frac{64}{9}

\frac{10000}{0.05} \cdot 1.0 5^{- 20} \cdot e^{- 0.06 \cdot 20}

3^{- 3} 0. 3^{1}

\frac{π}{2} e^{- 2 (0)}

x^{2} (m (m - 1) x^{m - 2})

What is (1/2)^2 1/((-1/4)^3)(2/3)^2 ?
The solution to (1/2)^2 1/((-1/4)^3)(2/3)^2 is -64/9