Math Problem Statement

Rewrite using a single exponent: (7^3)^3

Solution

The image shows an exponent problem: (73)3(7^3)^3.

To rewrite this expression using a single exponent, we can apply the Power of a Power Rule. This rule states:

(am)n=amn(a^m)^n = a^{m \cdot n}

For the given problem, this means:

(73)3=733=79(7^3)^3 = 7^{3 \cdot 3} = 7^9

So, the answer is 797^9.

Would you like more details or have any questions?

Here are some related questions for practice:

  1. How would you simplify (25)4(2^5)^4?
  2. What is the result of (32)6(3^2)^6 using the power rule?
  3. Can you apply the power rule to (x3)2(x^3)^2?
  4. How do you simplify (104)5(10^4)^5?
  5. What happens if the base is negative, e.g., (52)3(-5^2)^3?

Tip: When using the power of a power rule, always multiply the exponents, no matter what the base is.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Power Rule

Formulas

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

Theorems

Power of a Power Rule

Suitable Grade Level

Grades 7-9