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

The solution to (x^3)/2 (4x^{-1})^2 is 8x

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simplify (x^3)/2 (4x^{-1})^2

simplify

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

8 x

Solution steps

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

Simplify

(4 x^{- 1})^{2} : \frac{16}{x ^{2}}

= \frac{x ^{3}}{2} \cdot \frac{16}{x ^{2}}

Apply the fraction rule:

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

= \frac{x ^{3} \cdot 16}{2 x ^{2}}

Factor the number:

16 = 2 \cdot 8

= \frac{x ^{3} \cdot 2 \cdot 8}{2 x ^{2}}

Cancel the common factor:

2

= \frac{x ^{3} \cdot 8}{x ^{2}}

Simplify

\frac{x ^{3}}{x ^{2}} : x

= x \cdot 8

= 8 x

\frac{1}{2} (2 x^{2} - 8)^{2} + 8

a x^{2} + b x

lo g_{2} (0.6)

7 4^{2}

- 6 \cdot (- 9)