Math Problem Statement

Simplify: p * p^(-8). Express your answer as a single term, without a denominator.

Solution

The expression in the image is:

pp8p \cdot p^{-8}

To simplify this, we can use the property of exponents:

aman=am+na^m \cdot a^n = a^{m+n}

Here, the base is pp, and the exponents are 11 (since p=p1p = p^1) and 8-8.

Applying the exponent rule:

p1p8=p1+(8)=p7p^1 \cdot p^{-8} = p^{1 + (-8)} = p^{-7}

Thus, the simplified expression is:

p7p^{-7}

This is the final answer, expressed as a single term without a denominator.

Would you like further details or have any questions? Here are some related questions you might find helpful:

  1. What are the rules for multiplying powers with the same base?
  2. How can negative exponents be interpreted?
  3. What is the general rule for simplifying expressions with exponents?
  4. How would you handle a problem involving division of powers with the same base?
  5. What is the difference between multiplying and dividing terms with exponents?

Tip: When simplifying exponent expressions, always combine the exponents first when the bases are the same.

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Math Problem Analysis

Mathematical Concepts

Exponent Rules
Algebra

Formulas

a^m * a^n = a^(m+n)

Theorems

Exponentiation Theorem

Suitable Grade Level

Grades 6-9