foass77W

2021-02-21

Perform the indicated operation and express all answers with a rational denominator $2{a}^{2}b\sqrt[3]{4{a}^{3}b}\text{}\cdot \text{}-6a{b}^{2}\sqrt[3]{18a{b}^{4}}$

izboknil3

Skilled2021-02-22Added 99 answers

Given information:

The expression is$2{a}^{2}b\sqrt[3]{4{a}^{3}b}\text{}\cdot \text{}(-6a{b}^{2}\sqrt[3]{18a{b}^{4}}).$

Calculation:

Multiply the expression with out radicals with each other.

Use the law of exponents${a}^{b}\text{}\cdot \text{}{a}^{c}={a}^{b\text{}+\text{}c}$

$2{a}^{2}{b}^{3}\text{}\cdot \text{}(-6a{b}^{2}\sqrt[3]{18a{b}^{4}})\sqrt[3]{4{a}^{3}b}=\text{}-12{a}^{3}{b}^{5}(\sqrt[3]{18a{b}^{4}})\sqrt[3]{4{a}^{3}b}$

Multiply the expression with radicals with each other and use the law of exponents${a}^{b}\text{}\cdot \text{}{a}^{c}={a}^{b\text{}+\text{}c}$

$-12{a}^{3}{b}^{5}(\sqrt[3]{18a{b}^{4}})\sqrt[3]{4{a}^{3}b}=\text{}-12{a}^{3}{b}^{5}(\sqrt[3]{72{a}^{4}{b}^{5}})$

Finally answer:$-12{a}^{3}{b}^{5}\sqrt[3]{72{a}^{4}{b}^{5}}$

The expression is

Calculation:

Multiply the expression with out radicals with each other.

Use the law of exponents

Multiply the expression with radicals with each other and use the law of exponents

Finally answer:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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