Math Problem Statement

Simplify (x^5)^5.

Solution

The expression given is (x5)5(x^5)^5.

To simplify this, you can apply the power of a power rule, which states that (am)n=amn(a^m)^n = a^{m \cdot n}. In this case:

(x5)5=x55=x25(x^5)^5 = x^{5 \cdot 5} = x^{25}

So, the simplified form of the expression is:

x25x^{25}

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

Here are 5 related questions to deepen your understanding:

  1. How do you simplify expressions with multiple variables, such as (x3y2)4(x^3 y^2)^4?
  2. What is the difference between the power of a power rule and the product of powers rule?
  3. How do you simplify (xn)m(x^n)^m for general values of nn and mm?
  4. Can the power of a power rule be applied to roots, such as x4\sqrt{x^4}?
  5. How does exponentiation affect negative exponents, like (x2)3(x^{-2})^3?

Tip: Always remember to check the rules of exponents carefully when dealing with powers of powers or products of powers to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Power of a Power Rule

Formulas

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

Theorems

Exponentiation Theorem

Suitable Grade Level

Grades 7-9