Math Problem Statement

(x^6)^(5/4)

Solution

To simplify (x6)54(x^6)^{\frac{5}{4}}, we apply the power of a power rule: (am)n=amn(a^m)^n = a^{m \cdot n}.

So:

(x6)54=x654=x304=x7.5(x^6)^{\frac{5}{4}} = x^{6 \cdot \frac{5}{4}} = x^{\frac{30}{4}} = x^{7.5}

Thus, the simplified expression is:

x7.5x^{7.5}

Let me know if you'd like more details on this! Here are some related questions:

  1. How would you simplify (x3)23(x^3)^{\frac{2}{3}}?
  2. What is (x4)12(x^4)^{\frac{1}{2}}?
  3. How would you approach (x10)35(x^{10})^{\frac{3}{5}}?
  4. Can you simplify (x2)73(x^2)^{\frac{7}{3}}?
  5. What happens when simplifying (x8)56(x^8)^{\frac{5}{6}}?

Tip: When simplifying powers, always multiply the exponents together.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Exponentiation Rules

Formulas

(a^m)^n = a^{m * n}

Theorems

Power of a Power Rule

Suitable Grade Level

Grades 9-12