Exponents Math Example 5

Follow the full solution, then compare it with the other examples linked below.

Example 5

medium
Simplify 25×2324\frac{2^5 \times 2^3}{2^4}.

Solution

  1. 1
    Apply the product rule in the numerator: 25×23=25+3=282^5 \times 2^3 = 2^{5+3} = 2^8.
  2. 2
    Apply the quotient rule: 2824=28−4=24\frac{2^8}{2^4} = 2^{8-4} = 2^4.
  3. 3
    Evaluate: 24=162^4 = 16.

Answer

24=162^4 = 16
When multiplying powers with the same base, add the exponents. When dividing powers with the same base, subtract the exponents. These two rules together simplify most exponent expressions.

About Exponents

An operation representing repeated multiplication: ana^n means aa multiplied by itself nn times. For example, 23=2×2×2=82^3 = 2 \times 2 \times 2 = 8. Exponents extend to zero, negative, and fractional powers.

Learn more about Exponents →

More Exponents Examples

Example 1 easy

Compute [formula].

Example 2 medium

Simplify [formula].

Example 3 easy

Compute [formula].

Example 4 medium

Which is larger, [formula] or [formula]? Compute both to compare.

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