Exponent Rules Math Example 2

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Example 2

medium
Simplify (2x3y)4(2x^3y)^4.

Solution

  1. 1
    Apply the power rule to each factor: 24โ‹…(x3)4โ‹…y42^4 \cdot (x^3)^4 \cdot y^4.
  2. 2
    Evaluate: 24=162^4 = 16 and (x3)4=x12(x^3)^4 = x^{12}.
  3. 3
    Result: 16x12y416x^{12}y^4.

Answer

16x12y416x^{12}y^4
The power of a product rule states (ab)n=anbn(ab)^n = a^n b^n, and the power of a power rule states (am)n=amn(a^m)^n = a^{mn}. Apply both systematically to simplify expressions.

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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