What is \sqrt[4]{32^{2x}} ?

The solution to \sqrt[4]{32^{2x}} is (4sqrt(2))^x

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simplify \sqrt[4]{32^{2x}}

simplify

(42)^{x}

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

= 3 2^{2 x \frac{1}{4}}

Simplify

2 x \frac{1}{4} : \frac{x}{2}

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

Prime factorization of

32 : 2^{5}

= (2^{5})^{\frac{x}{2}}

Apply radical rule:

= (2^{5})^{x}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

Apply radical rule:

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

Apply radical rule:

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

= (2^{2} 2)^{x}

Refine

= (42)^{x}

x e^{- 3 x} (3 x e^{3 x})

\frac{e ^{3 x}}{e ^{7 x}}

6.2 \cdot 1 0^{- 1}

(6 s t u) (3 s t^{6} u)

- 0.3 e^{- 0.1}