Solved: "The simplest form of the expression, 40x4y73"

High School
Algebra
Pre-Algebra
Factors and multiples

melodykap

Answered question

2021-07-30

The simplest form of the expression, $\sqrt[3]{40 x^{4} y^{7}}$

Answer & Explanation

BleabyinfibiaG

Skilled2021-07-31Added 118 answers

Given: $\sqrt[3]{40 x^{4} y^{7}}$
Explanation:
We will make factors that have powers of 3 and its multiples because the index is 3.
Identifying perfect cube factors, we will get:
$\sqrt[3]{40 x^{4} y^{7}} = \sqrt[3]{5 \times 8 \times x^{3} \times x \times y^{6} \times y}$
Grouping the perfect cubes, we get:
$\sqrt[3]{40 x^{4} y^{7}} = \sqrt[3]{(8 x^{3} y^{6}) (5 x y)}$
Factoring into two radicals, we get:
$\sqrt[3]{40 x^{4} y^{7}} = \sqrt[3]{(8 x^{3} y^{6})} \times \sqrt[3]{(5 x y)}$
$\sqrt[3]{8} = 2$ and $\sqrt[3]{(x^{3} y^{6})} = x y^{2}$
$\sqrt[3]{40 x^{4} y^{7}} = 2 x y^{2} \sqrt[3]{(5 x y)}$
Therefore, the simplest form of the given expression $2 x y^{2} \sqrt[3]{(5 x y)}$

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