Wize High School Algebra I Textbook (Common Core) > Exponents & Radicals

Intro to Exponent Rules

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Exponent Rules
When simplifying an expression with powers, we could write it all out in terms of multiplication.

Example
23×2425\Large \dfrac{\bcf{2^3}\times\bcth{2^4}}{\bcfi{2^5}}2523×24​

=(2×2×2)×(2×2×2××2)(2×2×2×2×2)=\dfrac{\bcf{(2\times2\times2)}\times\bcth{(2\times2\times2\times\times2)}}{\bcfi{(2\times2\times2\times2\times2)}}=(2×2×2×2×2)(2×2×2)×(2×2×2××2)​

=8×1632=\dfrac{\bcf{8}\times\bcth{16}}{\bcfi{32}}=328×16​

Simplify by dividing numerator and denominator by 8:
=8 1×1632 4=\dfrac{\cancel{{8}}^{~1}\times{16}}{\cancel{{32}}^{~4}}=32 48​ 1×16​

=164=\dfrac{16}{4}=416​

Simplify by dividing numerator and denominator by 4:
=16 44 1=\dfrac{\cancel{16}^{~4}}{\cancel4^{~1}}=4​ 116 4​

=41=\dfrac{4}{1}=14​

=4=4=4

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This can be a lot of work sometimes! Luckily, we have some short-cuts that can help us out -- these are called the Exponent Rules or the Laws of Exponents.
Exponent rule for fractions & products
Product rule for multiplying powers
Quotient rule for dividing powers
Power of a power rule