Exponent Rules Math Example 1

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Example 1

easy
Simplify x5โ‹…x3x2\frac{x^5 \cdot x^3}{x^2}.

Solution

  1. 1
    Combine the factors in the numerator with the product rule: x5โ‹…x3=x5+3=x8x^5 \cdot x^3 = x^{5+3} = x^8.
  2. 2
    Rewrite the expression as x8x2\frac{x^8}{x^2} and apply the quotient rule for like bases.
  3. 3
    Subtract the exponents: x8โˆ’2=x6x^{8-2} = x^6.

Answer

x6x^6
The product rule says amโ‹…an=am+na^m \cdot a^n = a^{m+n}, and the quotient rule says aman=amโˆ’n\frac{a^m}{a^n} = a^{m-n}. These two laws handle most exponent simplifications.

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}).

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