Write the following expression in simplified radical form.
$\sqrt[4]{80 x^{8} y^{15}}$

Assume that all of the variables in the expression represent positive real numbers.
$◻$
$\sqrt{◻} \sqrt[◻]{◻}$

Answer

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Answer

$2 x^{2} y^{3} \sqrt[4]{5 y^{3}}$ is the final answer.

Steps

Step 1 ：The given expression is a fourth root. To simplify it, we need to find the factors of the number and the variables that are perfect fourth powers.

Step 2 ：For the number 80, the perfect fourth power factor is 16 (since $2^{4} = 16$ ).

Step 3 ：For the variable x, $x^{8}$ is a perfect fourth power since $(x^{2})^{4} = x^{8}$ .

Step 4 ：For the variable y, $y^{12}$ is a perfect fourth power since $(y^{3})^{4} = y^{12}$ .

Step 5 ：The remaining factors, 5 and $y^{3}$ , cannot be simplified further.

Step 6 ：Therefore, the simplified radical form of the expression is $2 x^{2} y^{3}$ times the fourth root of $5 y^{3}$ .

Step 7 ： $2 x^{2} y^{3} \sqrt[4]{5 y^{3}}$ is the final answer.

Write the following expression in simplified radical form.80x8y154 Assume that all of the variables in the expression represent positive real numbers.◻◻◻◻

Answer

Popular Problems

Write the following expression in simplified radical form.
$\sqrt[4]{80 x^{8} y^{15}}$

Assume that all of the variables in the expression represent positive real numbers.
$◻$
$\sqrt{◻} \sqrt[◻]{◻}$