Key Concepts

• Equivalent Fractions Property
  • If $a,b,c$ are whole numbers where $b\ne 0,c\ne 0$, then
    ${\Large\frac{a}{b}}={\Large\frac{a\cdot c}{b\cdot c}}$ and ${\Large\frac{a\cdot c}{b\cdot c}}={\Large\frac{a}{b}}$
• Zero Exponent
  • If $a$ is a non-zero number, then ${a}^{0}=1$.
  • Any nonzero number raised to the zero power is $1$.
• Quotient Property for Exponents
  • If $a$ is a real number, $a\ne 0$, and $m,n$ are whole numbers, then
    ${\Large\frac{{a}^{m}}{{a}^{n}}}={a}^{m-n},m>n$ and ${\Large\frac{{a}^{m}}{{a}^{n}}}={\Large\frac{1}{{a}^{n-m}}},n>m$
• Quotient to a Power Property for Exponents
  • If $a$ and $b$ are real numbers, $b\ne 0$, and $m$ is a counting number, then
    ${\Large{\left(\frac{a}{b}\right)}}^{m}={\Large\frac{{a}^{m}}{{b}^{m}}}$
  • To raise a fraction to a power, raise the numerator and denominator to that power.

Glossary

zero exponent

If $a$ is a non-zero number, then ${a}^{0}=1$ . Any nonzero number raised to the zero power is $1$.