"Rewrite with rational exponents: 5xy4 a3b25" was answered by our community

High School
Algebra
Algebra I
Exponents and radicals

ossidianaZ

Answered question

2021-10-18

Rewrite with rational exponents:
$\sqrt[4]{5 x y}$
$\sqrt[5]{\frac{a^{3} b}{2}}$

Answer & Explanation

tabuordg

Skilled2021-10-19Added 99 answers

We have to rewrite the rational exponents:
a. $\sqrt[4]{5 x y}$
b. $\sqrt[5]{\frac{a^{3} b}{2}}$
We know the properties of exponents,
$\sqrt[m]{a} = a^{\frac{1}{m}}$
${(a b)}^{m} = a^{m \times n}$
${(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$
Applying above prperties for the given expressions:
a. $\sqrt[4]{5 x y} = {(5 x y)}^{\frac{1}{4}}$
$= 5^{\frac{1}{4}} x^{\frac{1}{4}} y^{\frac{1}{4}}$
Hence, rewritten form of the rational exponent is $5^{\frac{1}{4}} x^{\frac{1}{4}} y^{\frac{1}{4}}$
b. $\sqrt[5]{\frac{a^{3} b}{2}} = {(\frac{a^{3} b}{2})}^{\frac{1}{5}}$
$= \frac{{(a^{3} b)}^{\frac{1}{5}}}{2^{\frac{1}{5}}}$
$= \frac{{(a^{3})}^{\frac{1}{5}} b^{\frac{1}{5}}}{2^{\frac{1}{5}}}$
Hence, rewritten form of the rational exponent is $\frac{{(a^{3})}^{\frac{1}{5}} b^{\frac{1}{5}}}{2^{\frac{1}{5}}}$

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