Math Problem Statement

(2x^9)^3

Solution

The given image shows the expression (2x9)3(2x^9)^3. Let's simplify this step by step:

Step-by-step solution:

  1. Apply the Power of a Power Rule: The general rule (am)n=amn(a^m)^n = a^{m \cdot n} applies here. So, for (x9)3(x^9)^3, we multiply the exponents: (x9)3=x93=x27(x^9)^3 = x^{9 \cdot 3} = x^{27}

  2. Distribute the exponent to the coefficient: Now apply the exponent to the constant 22. This follows the same principle: (2)3=8(2)^3 = 8

  3. Final Expression: Now combine the simplified terms: (2x9)3=8x27(2x^9)^3 = 8x^{27}

Final Answer:

8x278x^{27}

Let me know if you'd like further explanation or have any other questions!

Here are 5 questions based on this solution:

  1. How does the power rule apply to both numbers and variables in an expression?
  2. What happens when you have an expression like (xm)n(x^m)^n?
  3. How do you simplify (3x2)4(3x^2)^4 using the same rules?
  4. How would the process change if the expression was (2x9)2(2x^9)^2 instead?
  5. What is the difference between the power of a product rule and the power of a power rule?

Tip: Always distribute exponents carefully across both coefficients and variables!

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponentiation
Power of a Product Rule

Formulas

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

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-10