Math Problem Statement

Simplify (-512)^(1/3)

Solution

To simplify (512)13(-512)^{\frac{1}{3}}, we need to find the cube root of 512-512.

  1. Identify the cube root: The cube root of a number a13a^{\frac{1}{3}} is a value that, when raised to the power of 3, results in aa.

  2. Calculate the cube root of -512: (512)13=8(-512)^{\frac{1}{3}} = -8 because (8)×(8)×(8)=512(-8) \times (-8) \times (-8) = -512.

Answer: (512)13=8(-512)^{\frac{1}{3}} = -8.

Would you like further details or have any questions?

Here are five related questions you might be interested in:

  1. What is the cube root of a positive number, like 51213512^{\frac{1}{3}}?
  2. How does taking an even root differ from taking an odd root of a negative number?
  3. How would you calculate (512)23(-512)^{\frac{2}{3}}?
  4. What are some applications of cube roots in real-world problems?
  5. How do you simplify other fractional exponents, like 641664^{\frac{1}{6}}?

Tip: When taking odd roots of negative numbers, the result is also negative, as shown here with (512)13=8(-512)^{\frac{1}{3}} = -8.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Roots

Formulas

a^(1/n) represents the n-th root of a

Theorems

Cube root theorem

Suitable Grade Level

Grades 8-10