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

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

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

simplify

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

\frac{1}{4 x}

Solution steps

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

Simplify

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

= 4 x^{3} \frac{1}{16 x ^{4}}

Apply the fraction rule:

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

= \frac{4 x ^{3} \cdot 1}{16 x ^{4}}

Multiply the numbers:

4 \cdot 1 = 4

= \frac{4 x ^{3}}{16 x ^{4}}

Factor the number:

16 = 4 \cdot 4

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

Cancel the common factor:

4

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

Simplify

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

= \frac{1}{4 x}

90 \times 3

+ x^{3} + 2 x^{2} + 5 x + 10

121 - 144 x^{2}

2 \frac{1}{2} \times 4

- 3 \times 2 x