Exponent Rules Math Example 3

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

Example 3

medium
Simplify (3a2)39a4\frac{(3a^2)^3}{9a^4}.

Solution

  1. 1
    Expand the numerator: (3a2)3=27a6(3a^2)^3 = 27a^6.
  2. 2
    Divide: 27a69a4=3a6โˆ’4=3a2\frac{27a^6}{9a^4} = 3a^{6-4} = 3a^2.

Answer

3a23a^2
Expand powers first, then apply the quotient rule for both coefficients and variable parts separately.

About Exponent Rules

A set of laws governing how exponents behave under multiplication, division, and raising to a power: product rule (amโ‹…an=am+na^m \cdot a^n = a^{m+n}), quotient rule (am/an=amโˆ’na^m / a^n = a^{m-n}), power rule ((am)n=amn(a^m)^n = a^{mn}), zero exponent (a0=1a^0 = 1 for aโ‰ 0a \neq 0), and negative exponent (aโˆ’n=1ana^{-n} = \frac{1}{a^n}).

Learn more about Exponent Rules โ†’

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