Question
Find the indicated root. \( \sqrt[3]{x^{15}} \) \( x \)
Ask by Moreno Lindsey. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The cube root of \( x^{15} \) simplifies to \( x^5 \).
Solution
To simplify the expression, write the cube root as an exponent:
∛(x¹⁵) = (x¹⁵)^(1/3)
Multiply the exponents:
(x¹⁵)^(1/3) = x^(15/3) = x⁵
Thus, the simplified expression is x⁵.
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Simplify this solution The Deep Dive
Did you know that the cube root of a number is equivalent to raising that number to the power of one-third? So, when we take \( \sqrt[3]{x^{15}} \), it’s the same as \( x^{15/3} \). Simplifying that fraction gives us \( x^5 \)! Isn't it great how exponents work? In the real world, cube roots are particularly useful when dealing with volume. For instance, if you're building a cube-shaped garden, and you know the volume in cubic feet, taking the cube root will easily tell you how long each side of the cube should be. Mathematics is not just for the classroom; it's all around us!
