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IgorC [24]
3 years ago
15

Simplify the expression and rewrite in rational exponent form.

Mathematics
1 answer:
Dahasolnce [82]3 years ago
5 0

Answer:

4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}

Step-by-step explanation:

The given expression: 4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}}

Step 1: Change radical to fractional exponent.

Formula for fractional exponent: \sqrt[n]{a}=a^{\frac{1}{n}}

The power to which the base is raised becomes the numerator and the root becomes the denominator.

\Rightarrow 4 x^{\frac{3}{5}} \cdot y^{4} \cdot x^{\frac{1}{2}} \cdot y^{\frac{5}{3}}  

Step 2: Apply law of exponent for a product a^{m} \times a^{n}=a^{m+n}  

Multiply powers with same base.

\Rightarrow 4 x^{\frac{3}{5}+\frac{1}{2}} \cdot y^{4+\frac{5}{8}}  

Take LCM for the fractions in the power.

\Rightarrow 4 x^{\frac{6}{10}+\frac{5}{10}} \cdot y^{\frac{12}{3}+\frac{5}{3}}  

\Rightarrow 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}

Hence the simplified form of 4 \sqrt[5]{x^{3}} \cdot y^{4} \cdot \sqrt{x} \cdot \sqrt[3]{y^{5}} \text { is } 4 x^{\frac{11}{10}} \cdot y^{\frac{17}{3}}.

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