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This page is worth 2 points.
Express the radicals in simplified rational exponent form.

root(4)(8)=

◻

root(3)(200)=

◻ .
◻

$1$ $\newline$ $2$ $\newline$ $3$ $\newline$ $4$ $\newline$ $5$ $\newline$ $6$ $\newline$ $7$ $\newline$ $8$ $\newline$ $9$ $\newline$ This page is worth $2$ points. $\newline$ Express the radicals in simplified rational exponent form. $\newline$ $\sqrt[4]{8}=$ $\newline$ $\square$ $\newline$ $\sqrt[3]{200}=$ $\newline$ $\square$ . $\square$

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Multiply radical expressions

Full solution

Q.

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This page is worth

2

points.

\newline

Express the radicals in simplified rational exponent form.

\newline

\sqrt[4]{8}=

\newline

\square

\newline

\sqrt[3]{200}=

\newline

\square

.

\square

Apply Fourth Root: For $\sqrt[4]{8}$ , express $8$ as $2^3$ and apply the fourth root. $\newline$ $\sqrt[4]{8} = \sqrt[4]{2^3} = (2^3)^{\frac{1}{4}}$ .
Simplify Exponent: Simplify the exponent by multiplying $3$ by $\frac{1}{4}$ . $\$2^3$ ^{\frac{ $1$ }{ $4$ }} = $2$ ^{\frac{ $3$ }{ $4$ }}\).
Apply Cube Root: For $\sqrt[3]{200}$ , express $200$ as $2^3 \times 5^2$ and apply the cube root. $\newline$ $\sqrt[3]{200} = \sqrt[3]{2^3 \times 5^2} = (2^3)^{1/3} \times (5^2)^{1/3}$ .
Simplify Exponents: Simplify the exponents by multiplying $3$ by $1/3$ and $2$ by $1/3$ . $\newline$ $(2^3)^{1/3} \times (5^2)^{1/3} = 2^{3/3} \times 5^{2/3}.$
Further Simplify Exponents: Simplify the exponents further. $\newline$ $2^{\frac{3}{3}} \times 5^{\frac{2}{3}} = 2^1 \times 5^{\frac{2}{3}} = 2 \times 5^{\frac{2}{3}}$ .

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