What is (ab\sqrt[3]{2a^2b})(2b\sqrt[3]{4a^2b}) ?

The solution to (ab\sqrt[3]{2a^2b})(2b\sqrt[3]{4a^2b}) is 2\sqrt[3]{2}*2^{2/3}a^{7/3}b^{8/3}

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simplify (ab\sqrt[3]{2a^2b})(2b\sqrt[3]{4a^2b})

simplify

Solution steps

Apply exponent rule:

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

bb = b^{1 + 1}

Add the numbers:

1 + 1 = 2

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

Apply exponent rule:

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

Factor integer

4 = 2^{2}

Apply exponent rule:

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

Refine

(a^{2} b)^{\frac{1}{3} + \frac{1}{3}} : a^{\frac{4}{3}} b^{\frac{1}{3} + \frac{1}{3}}

Apply exponent rule:

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

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

b^{2 + \frac{1}{3} + \frac{1}{3}} = b^{\frac{8}{3}}

Apply exponent rule:

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

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

a^{1 + \frac{4}{3}} = a^{\frac{7}{3}}

e^{- 0.119}

2 e^{t} e^{- t}

(\frac{1}{4})^{\frac{1}{2}} \cdot (0.1)^{- 2}

7.698 \cdot 1 0^{- 3}

x^{3 x} (\frac{3}{2} + \frac{3}{2} ln (x))

What is (ab\sqrt[3]{2a^2b})(2b\sqrt[3]{4a^2b}) ?
The solution to (ab\sqrt[3]{2a^2b})(2b\sqrt[3]{4a^2b}) is 2\sqrt[3]{2}*2^{2/3}a^{7/3}b^{8/3}