Given x > 0, the expression root(5)(x^(15)) is equivalent to x^(3) x^(2) x^(2)root(5)(x^(3)) x^(3)root(5)(x^(3))

Rewrite expression as power: We are given the expression root(5)(x^(15)) and we need to simplify it. The 5th root of a number is the same as raising that number to the power of 1/5. So, we can rewrite the expression as (x^(15))^(1/5).Apply exponent property: Using the property of exponents that (a^m)^n = a^(m*n), we can simplify the expression further. We multiply the exponents 15 and 1/5 together.Calculate exponent product: Calculating the product of the exponents gives us 15 * (1/5) = 3. So, the expression becomes x^(15*(1/5)) which is x^3.Final simplified expression: Since x > 0, we don't need to worry about the expression being undefined or taking an even root of a negative number. Therefore, the simplified expression is x^3.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given
x > 0, the expression
root(5)(x^(15)) is equivalent to

x^(3)

x^(2)

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

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

Given x>0 , the expression $\sqrt[5]{x^{15}}$ is equivalent to $\newline$ $x^{3}$ $\newline$ $x^{2}$ $\newline$ $x^{2} \sqrt[5]{x^{3}}$ $\newline$ $x^{3} \sqrt[5]{x^{3}}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

\sqrt[5]{x^{15}}

is equivalent to

\newline

x^{3}

\newline

x^{2}

\newline

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

\newline

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

Rewrite expression as power: We are given the expression $\sqrt[5]{x^{15}}$ and we need to simplify it. The $5^{\text{th}}$ root of a number is the same as raising that number to the power of $\frac{1}{5}$ . So, we can rewrite the expression as $(x^{15})^{\frac{1}{5}}$ .
Apply exponent property: Using the property of exponents that $(a^m)^n = a^{m*n}$ , we can simplify the expression further. We multiply the exponents $15$ and $\frac{1}{5}$ together.
Calculate exponent product: Calculating the product of the exponents gives us $15 \times (1/5) = 3$ . So, the expression becomes $x^{15\times(1/5)}$ which is $x^3$ .
Final simplified expression: Since x > 0, we don't need to worry about the expression being undefined or taking an even root of a negative number. Therefore, the simplified expression is $x^3$ .