Given x > 0, the expression root(3)(x^(32)) is equivalent to x^(10)root(3)(x) x^(11)root(3)(x^(2)) x^(11)root(3)(x) x^(10)root(3)(x^(2))

Understand the expression: Understand the expression root(3)(x^(32)). The expression root(3)(x^(32)) means the cube root of x raised to the 32nd power.Apply exponent property: Apply the property of exponents to simplify the cube root. The cube root of x raised to the 32nd power can be written as x^(32/3).Divide exponent by 3: Divide the exponent by 3 to separate the whole number part and the remainder. 32 divided by 3 gives 10 with a remainder of 2, so x^(32/3) can be written as x^(10 + 2/3).Separate into two parts: Separate the expression into two parts: the whole number exponent and the fractional exponent. This gives us x^(10) * x^(2/3).Recognize x^(2/3): Recognize that x^(2/3) is the cube root of x squared. We can rewrite x^(2/3) as root(3)(x^(2)).Combine expressions: Combine the expressions to get the final equivalent expression. The final expression is x^(10) * root(3)(x^(2)), which is x^(10)root(3)(x^(2)).

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Given
x > 0, the expression
root(3)(x^(32)) is equivalent to

x^(10)root(3)(x)

x^(11)root(3)(x^(2))

x^(11)root(3)(x)

x^(10)root(3)(x^(2))

Given x>0 , the expression $\sqrt[3]{x^{32}}$ is equivalent to $\newline$ $x^{10} \sqrt[3]{x}$ $\newline$ $x^{11} \sqrt[3]{x^{2}}$ $\newline$ $x^{11} \sqrt[3]{x}$ $\newline$ $x^{10} \sqrt[3]{x^{2}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

\sqrt[3]{x^{32}}

is equivalent to

\newline

x^{10} \sqrt[3]{x}

\newline

x^{11} \sqrt[3]{x^{2}}

\newline

x^{11} \sqrt[3]{x}

\newline

x^{10} \sqrt[3]{x^{2}}

Understand the expression: Understand the expression $\sqrt[3]{x^{32}}$ . The expression $\sqrt[3]{x^{32}}$ means the cube root of $x$ raised to the $32$ nd power.
Apply exponent property: Apply the property of exponents to simplify the cube root. $\newline$ The cube root of $x$ raised to the $32^{\text{nd}}$ power can be written as $x^{(32/3)}$ .
Divide exponent by $3$ : Divide the exponent by $3$ to separate the whole number part and the remainder. $\newline$ $32$ divided by $3$ gives $10$ with a remainder of $2$ , so $x^{(32/3)}$ can be written as $x^{(10 + 2/3)}$ .
Separate into two parts: Separate the expression into two parts: the whole number exponent and the fractional exponent. $\newline$ This gives us $x^{10} \times x^{\frac{2}{3}}$ .
Recognize $x^{\frac{2}{3}}$ : Recognize that $x^{\frac{2}{3}}$ is the cube root of $x$ squared. $\newline$ We can rewrite $x^{\frac{2}{3}}$ as $\sqrt[3]{x^{2}}$ .
Combine expressions: Combine the expressions to get the final equivalent expression. $\newline$ The final expression is $x^{10} \cdot \sqrt[3]{x^{2}}$ , which is $x^{10}\sqrt[3]{x^{2}}$ .