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

The solution to (2x^2)^{-2}*(2x^4)^2 is x^4

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

simplify

(2 x^{2})^{- 2} \cdot (2 x^{4})^{2}

x^{4}

Solution steps

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

Simplify

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

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

Simplify

(2 x^{4})^{2} : 4 x^{8}

= \frac{1}{4 x ^{4}} \cdot 4 x^{8}

Apply the fraction rule:

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

= \frac{1 \cdot 4 x ^{8}}{4 x ^{4}}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4 x ^{8}}{4 x ^{4}}

Cancel the common factor:

4

= \frac{x ^{8}}{x ^{4}}

Simplify

\frac{x ^{8}}{x ^{4}} : x^{4}

= x^{4}

- x^{2} - 2 x \leq - 3

6 x^{2} - 12 x = 0

- 3 < x < 7

e^{4 x - 2} \geq 16

3 + 2 x = - x + 1