Exponent Rules Math Example 4

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

Example 4

medium
Simplify (2m3)24m\frac{(2m^3)^2}{4m}.

Solution

  1. 1
    Apply the power rule: (2m3)2=4m6(2m^3)^2 = 4m^6.
  2. 2
    Divide by 4m4m: 4m64m=m6โˆ’1=m5\frac{4m^6}{4m} = m^{6-1} = m^5.

Answer

m5m^5
Use the power rule first, then simplify the quotient by dividing coefficients and subtracting exponents on like bases.

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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