Expert answers to "The simplified form of the expression cd24×c2d3."

Khaleesi Herbert

Answered question

2021-01-05

The simplified form of the expression

\sqrt[4]{c d^{2}} \times \sqrt[3]{c^{2} d} .

grbavit

Skilled2021-01-06Added 109 answers

Formula used:
Product property of radicals:
If a and b are real numbers and

n > 1

is an integer, the product property is true provided that the radicals are real numbers.

\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{a b}

If m and n are integers and

n > 1

is an integer, then

\sqrt[n]{a^{m}} = a^{m n}

Calculation:
Consider the expression,

\sqrt[4]{c d^{2}} \times \sqrt[3]{c^{2} d}

Rewrite the provided expression as rational exponents.

\sqrt[4]{c d^{2}} \times \sqrt[3]{c^{2} d} = {(c d^{2})}^{1 / 4} \times {(c^{2} d)}^{1 / 3}

Use the product property.

{(c d^{2})}^{1 / 4} \times {(c^{2} d)}^{1 / 3} = {(c)}^{1 / 4} \times {(d^{2})}^{1 / 4} \times {(c^{2})}^{1 / 3} \times {(d)}^{1 / 3}

Use the formula

\sqrt[n]{a^{m}} = a^{m / n}

and simplify the expression.

{(c)}^{1 / 4} \times {(d^{2})}^{1 / 4} \times {(c^{2})}^{1 / 3} \times {(d)}^{1 / 3} = c^{1 / 4} \times d^{2 / 4} \times c^{2 / 3} \times d^{1 / 3}

Add the powers of the same bases.

c^{1 / 4} \times d^{2 / 4} \times c^{2 / 3} \times d^{1 / 3} = c (\frac{1}{4}) + (\frac{2}{4}) \times d (\frac{2}{4}) + (\frac{1}{3})

= c^{\frac{11}{12}} \times d^{\frac{10}{12}}

The obtained expression with rational exponents can be rewritten into radicals as,

= c^{\frac{11}{12}} \times d^{\frac{10}{12}} = {(c^{11})}^{\frac{1}{12}} \times {(d^{10})}^{\frac{1}{12}}

= \sqrt[12]{c^{11} d^{10}}

Answer:

\sqrt[4]{c d^{2}} \times \sqrt[3]{c^{2} d} i s \sqrt[12]{c^{11} d^{10}}

Jeffrey Jordon

Expert2021-10-26Added 2605 answers

Answer is given below (on video)

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