To calculate: The simplified value of the expression 32x16y105 using radical notation.

Formula used: From the product rule, abn=an⋅bn Where a and b are positive number and n is larger than 1. Calculation: Consider the provided expression, 32x16y105 Expand the expression by identifying the largest exponents and multiples of 5, 32x16y105=25⋅x15⋅x⋅y105 Now, separate the terms with fifth power factors by using the product rule, 25⋅x15⋅x⋅y105=255⋅x155⋅x5⋅y105 Simplify it further, 255⋅x155⋅x5⋅y105=2⋅x3⋅x5⋅y2 =2x3y2x5 Hence, the simplified value of expression is 2x3y2x5

Solved: "To calculate: The simplified value of the expression..."

High School
Algebra
Pre-Algebra
Factors and multiples

Alyce Wilkinson

Answered question

2021-08-03

To calculate: The simplified value of the expression $\sqrt[5]{32 x^{16} y^{10}}$ using radical notation.

Answer & Explanation

lamusesamuset

Skilled2021-08-04Added 93 answers

Formula used:
From the product rule,
$\sqrt[n]{a b} = \sqrt[n]{a} \cdot \sqrt[n]{b}$
Where a and b are positive number and n is larger than 1.
Calculation:
Consider the provided expression,
$\sqrt[5]{32 x^{16} y^{10}}$
Expand the expression by identifying the largest exponents and multiples of 5,
$\sqrt[5]{32 x^{16} y^{10}} = \sqrt[5]{2^{5} \cdot x^{15} \cdot x \cdot y^{10}}$
Now, separate the terms with fifth power factors by using the product rule,
$\sqrt[5]{2^{5} \cdot x^{15} \cdot x \cdot y^{10}} = \sqrt[5]{2^{5}} \cdot \sqrt[5]{x^{15}} \cdot \sqrt[5]{x} \cdot \sqrt[5]{y^{10}}$
Simplify it further,
$\sqrt[5]{2^{5}} \cdot \sqrt[5]{x^{15}} \cdot \sqrt[5]{x} \cdot \sqrt[5]{y^{10}} = 2 \cdot x^{3} \cdot \sqrt[5]{x} \cdot y^{2}$
$= 2 x^{3} y^{2} \sqrt[5]{x}$
Hence, the simplified value of expression is $2 x^{3} y^{2} \sqrt[5]{x}$

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