Given x > 0, the expression root(3)(x^(18)) is equivalent to x^(5)root(3)(x^(2)) x^(6) x^(6)root(3)(x^(2)) x^(5)

Rewrite expression: We are given the expression root(3)(x^(18)) and we need to simplify it. The cube root of a number is the same as raising that number to the power of 1/3. So, we can rewrite the expression as: x^(18)^(1/3)Apply power rule: Now we apply the power rule for exponents, which states that (a^(m))^n = a^(m*n). In this case, we have: x^(18*1/3)Multiply exponents: Multiplying the exponents, we get: x^(18/3)Divide and simplify: Dividing 18 by 3, we find the simplified exponent: x^(6)Final expression: Since x > 0, x^(6) is a valid expression and there is no need for absolute value or further simplification. Therefore, the equivalent expression for root(3)(x^(18)) is x^(6).

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Given
x > 0, the expression
root(3)(x^(18)) is equivalent to

x^(5)root(3)(x^(2))

x^(6)

x^(6)root(3)(x^(2))

x^(5)

Given x>0 , the expression $\sqrt[3]{x^{18}}$ is equivalent to $\newline$ $x^{5} \sqrt[3]{x^{2}}$ $\newline$ $x^{6}$ $\newline$ $x^{6} \sqrt[3]{x^{2}}$ $\newline$ $x^{5}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

\sqrt[3]{x^{18}}

is equivalent to

\newline

x^{5} \sqrt[3]{x^{2}}

\newline

x^{6}

\newline

x^{6} \sqrt[3]{x^{2}}

\newline

x^{5}

Rewrite expression: We are given the expression $\sqrt[3]{x^{18}}$ and we need to simplify it. The cube root of a number is the same as raising that number to the power of $\frac{1}{3}$ . So, we can rewrite the expression as: $x^{18^{\frac{1}{3}}}$
Apply power rule: Now we apply the power rule for exponents, which states that $(a^{m})^{n} = a^{m*n}$ . In this case, we have: $x^{18*\frac{1}{3}}$
Multiply exponents: Multiplying the exponents, we get: $x^{\frac{18}{3}}$
Divide and simplify: Dividing $18$ by $3$ , we find the simplified exponent: $x^{6}$
Final expression: Since x > 0, $x^{6}$ is a valid expression and there is no need for absolute value or further simplification. Therefore, the equivalent expression for $\sqrt[3]{x^{18}}$ is $x^{6}$ .