Math Problem Statement

Simplify.

Simplify the expression 3^2 * 3^(-5).

Solution

The expression shown in the image is:

32353^2 \cdot 3^{-5}

To simplify this, we use the property of exponents that states:

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

Here, both terms have the same base (3), so we can add the exponents:

3235=32+(5)=333^2 \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3}

Now, 333^{-3} can be written as:

133=127\frac{1}{3^3} = \frac{1}{27}

Thus, the simplified result is:

127\frac{1}{27}

Would you like more details or have any questions?

Here are 5 related questions to explore:

  1. What happens if the base is different, but the exponents are the same?
  2. How do we handle negative exponents in other expressions?
  3. Can you simplify 23242^3 \cdot 2^{-4}?
  4. What is the general rule for dividing terms with the same base and exponents?
  5. How do fractional exponents work when simplifying?

Tip: Always check if bases are the same when multiplying or dividing terms with exponents, as it allows for easy simplification!

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Math Problem Analysis

Mathematical Concepts

Exponents
Algebra

Formulas

a^m * a^n = a^(m+n)
Negative exponents: a^(-n) = 1 / a^n

Theorems

Exponentiation properties

Suitable Grade Level

Grades 6-8