What is (16x^2)^{1/3}(\sqrt[3]{4x}) ?

The solution to (16x^2)^{1/3}(\sqrt[3]{4x}) is 4x

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simplify (16x^2)^{1/3}(\sqrt[3]{4x})

simplify

4 x

Solution steps

Apply rule:

(a) = a

Simplify

(16 x^{2})^{\frac{1}{3}} : 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}}

Simplify

Apply radical rule:

Simplify

x^{\frac{2}{3}} x^{\frac{1}{3}} : x

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

Factor integer

4 = 2^{2}

Apply exponent rule:

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

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

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

Refine

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

Apply exponent rule:

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

2^{\frac{4}{3}} \cdot 2^{\frac{2}{3}} = 2^{\frac{4}{3} + \frac{2}{3}}

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

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

= 2^{2} x

2^{2} = 4

= 4 x

\frac{π}{2} S (\frac{2}{π} \cdot 4)

\frac{5}{2} e^{- \frac{5}{2}}

(5 x^{4}) (3 x^{5})

(- 2 + 1) e^{- 2}

(33) (23)

What is (16x^2)^{1/3}(\sqrt[3]{4x}) ?
The solution to (16x^2)^{1/3}(\sqrt[3]{4x}) is 4x