What is \sqrt[3]{3328}^2\sqrt[3]{416}pi ?

The solution to \sqrt[3]{3328}^2\sqrt[3]{416}pi is 128*13^{2/3}\sqrt[3]{13}pi

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simplify \sqrt[3]{3328}^2\sqrt[3]{416}pi

simplify

Decimal Notation

5227.61017 \dots

Solution steps

Factor integer

3328 = 2^{8} \cdot 13

Apply exponent rule:

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

(2^{8} \cdot 13)^{\frac{2}{3}} = (2^{8})^{\frac{2}{3}} \cdot 1 3^{\frac{2}{3}}

Apply exponent rule:

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

(2^{8})^{\frac{2}{3}} = 2^{8 \cdot \frac{2}{3}}

Refine

Factor integer

416 = 2^{5} \cdot 13

Apply radical rule:

Apply exponent rule:

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

Refine

Apply exponent rule:

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

2^{\frac{16}{3}} \cdot 2^{\frac{5}{3}} = 2^{\frac{16}{3} + \frac{5}{3}}

2^{\frac{16}{3} + \frac{5}{3}} = 2^{7}

2^{7} = 128

7 \cdot e^{- 6}

4 - x^{2} 1 + \frac{x ^{2}}{4 - x ^{2}}

e^{- (1.1)^{2}}

(\frac{50}{6.425 \cdot 1 0 ^{- 3}}) \cdot 1 0^{- 6}

(1 - 3 \cdot 0.75) \cdot e^{- 3 \cdot 0.75}

What is \sqrt[3]{3328}^2\sqrt[3]{416}pi ?
The solution to \sqrt[3]{3328}^2\sqrt[3]{416}pi is 128*13^{2/3}\sqrt[3]{13}pi