Given x > 0, the expression root(4)(x^(8)) is equivalent to x xroot(4)(x^(2)) x^(2)root(4)(x^(2)) x^(2)

Understand the expression: Understand the expression root(4)(x^(8)). The expression root(4)(x^(8)) means the 4th root of x raised to the 8th power.Apply property of exponents: Apply the property of exponents for roots. The 4th root of x^8 can be written as (x^8)^(1/4).Simplify using power rule: Simplify the expression using the power of a power rule. Using the power of a power rule, we multiply the exponents: (x^8)^(1/4) = x^(8*(1/4)).Calculate new exponent: Calculate the new exponent. 8 multiplied by 1/4 is 2, so x^(8*(1/4)) = x^2.Write final expression: Write the final simplified expression. The equivalent expression for root(4)(x^(8)) is x^2.

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Given
x > 0, the expression
root(4)(x^(8)) is equivalent to

x

xroot(4)(x^(2))

x^(2)root(4)(x^(2))

x^(2)

Given x>0 , the expression $\sqrt[4]{x^{8}}$ is equivalent to $\newline$ $x$ $\newline$ $x \sqrt[4]{x^{2}}$ $\newline$ $x^{2} \sqrt[4]{x^{2}}$ $\newline$ $x^{2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

\sqrt[4]{x^{8}}

is equivalent to

\newline

x

\newline

x \sqrt[4]{x^{2}}

\newline

x^{2} \sqrt[4]{x^{2}}

\newline

x^{2}

Understand the expression: Understand the expression $\sqrt[4]{x^{8}}$ . The expression $\sqrt[4]{x^{8}}$ means the $4$ th root of $x$ raised to the $8$ th power.
Apply property of exponents: Apply the property of exponents for roots. $\newline$ The $4^{\text{th}}$ root of $x^8$ can be written as $(x^8)^{\frac{1}{4}}$ .
Simplify using power rule: Simplify the expression using the power of a power rule. $\newline$ Using the power of a power rule, we multiply the exponents: $(x^8)^{\frac{1}{4}} = x^{8*\left(\frac{1}{4}\right)}$ .
Calculate new exponent: Calculate the new exponent. $8$ multiplied by $\frac{1}{4}$ is $2$ , so $x^{(8*(\frac{1}{4}))} = x^2$ .
Write final expression: Write the final simplified expression. $\newline$ The equivalent expression for $\sqrt[4]{x^{8}}$ is $x^2$ .