Solved: "Perform the indicated operation and express all answers..."

High School
Algebra
Algebra I
Exponents and radicals

glamrockqueen7

Answered question

2021-09-19

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

Answer & Explanation

Lacey-May Snyder

Skilled2021-09-20Added 88 answers

Given information:
The expression is $2 a^{2} b \sqrt[3]{4 a^{3} b} \cdot - 6 a b^{2} \sqrt[3]{18 a b^{4}}$
Calculation:
Multiply the expression with out radicals with each other.
Use the law of exponents $a^{b} \cdot a^{c} = a^{b + c}$
$2 a^{2} b^{3} \cdot (- 6 a b^{2} \sqrt[3]{18 a b^{4}}) \sqrt[3]{4 a^{3} b} = - 12 a^{3} b^{5} (\sqrt[3]{18 a b^{4}}) \sqrt[3]{4 a^{3} b}$
Multiply the expression with radicals with each other and use the law of exponents $a^{b} \cdot a^{c} = a^{b + c}$
$- 12 a^{3} b^{5} (\sqrt[3]{18 a b^{4}}) \sqrt[3]{4 a^{3} b} = - 12 a^{3} b^{5} (\sqrt[3]{72 a^{4} b^{5}})$
Answer: $- 12 a^{3} b^{5} (\sqrt[3]{72 a^{4} b^{5}})$

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