What is \sqrt[3]{4}\times \sqrt[6]{16} ?

The solution to \sqrt[3]{4}\times \sqrt[6]{16} is 2\sqrt[3]{2}

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simplify \sqrt[3]{4}\times \sqrt[6]{16}

simplify

Decimal Notation

2.51984 \dots

Solution steps

Factor integer

4 = 2^{2}

Apply exponent rule:

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

Refine

Factor integer

16 = 2^{4}

Apply exponent rule:

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

= 2^{\frac{2}{3}} \cdot 2^{4 \cdot \frac{1}{6}}

Refine

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

Apply exponent rule:

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

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

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

Add similar elements:

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

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

Multiply

2 \cdot \frac{2}{3} : \frac{4}{3}

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

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

= 2^{1 + \frac{1}{3}}

Apply exponent rule:

x^{a + b} = x^{a} x^{b}

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

Refine

\frac{7 x ^{2} - 28 x}{x ^{2} - 16}

(3 x + 2) (5 x + 4)

- 6 x^{2} y^{2} - 15 x^{2} y - 9 x^{2}

(t - 2) (t + 5) (t - 4)

38 \cdot 103

What is \sqrt[3]{4}\times \sqrt[6]{16} ?
The solution to \sqrt[3]{4}\times \sqrt[6]{16} is 2\sqrt[3]{2}