Math Problem Statement

Evaluate \placeholder364m3\placeholder{}^3\sqrt{64m^3}

Solution

To evaluate the expression 64m33\sqrt[3]{64m^3}, follow these steps:

  1. Factor the expression inside the cube root: 64m3=64×m364m^3 = 64 \times m^3

  2. Calculate the cube root of each factor separately:

    • 643\sqrt[3]{64}: The cube root of 64 is 4 because 43=4×4×4=644^3 = 4 \times 4 \times 4 = 64.
    • m33\sqrt[3]{m^3}: The cube root of m3m^3 is mm because (m)3=m3(m)^3 = m^3.
  3. Combine the results: 64m33=4m\sqrt[3]{64m^3} = 4m

Thus, the evaluated expression is 4m\boxed{4m}.

Would you like more details, or do you have any questions?


Here are five related questions to explore:

  1. What is the cube root of 125m6125m^6?
  2. How would you evaluate 81n44\sqrt[4]{81n^4}?
  3. If m=2m = 2, what is the value of ( \

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Cube roots
Exponentiation
Algebra

Formulas

-

Theorems

-

Suitable Grade Level

Grades 7-9