Math Problem Statement

a^{-2}\cdot a^5\cdot a^{-3}

Solution

To simplify the expression a2a5a3a^{-2} \cdot a^5 \cdot a^{-3}, we use the property of exponents that states:

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

  1. Combine the exponents by adding them:

a2+53=a0a^{-2 + 5 - 3} = a^0

  1. Since a0=1a^0 = 1 for any non-zero aa:

a0=1a^0 = 1

So, the simplified expression is 11.

Would you like more details on exponent rules, or have any questions?

Here are some related questions:

  1. How do we simplify expressions with multiple variables and exponents?
  2. What happens if the base aa equals 0?
  3. How does division work with exponents, such as aman\frac{a^m}{a^n}?
  4. What are fractional exponents, and how do they work?
  5. How can you handle negative exponents in fractions?

Tip: When multiplying terms with the same base, always add the exponents.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Exponent Rules

Formulas

a^m \cdot a^n = a^{m+n}
a^0 = 1

Theorems

Exponent Addition Rule
Zero Exponent Rule

Suitable Grade Level

Grades 6-8