Simplify the expression and rewrite in rational exponent

Ответ:

thunder42

15.01.2022

Mathematics

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

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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Ответ:

mbonham481

12.11.2020

Mathematics

4.178 times 10 to the power 2

Explanation:

Scientific notation has one number before the decimal place. This can be moved by figuring out how many places the decimal needs to move. Since this problem calls for it to move 2 places to the left, the exponent is 2.

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Simplify the expression and rewrite in rational exponent form.

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