Summary: Dividing Monomials

Key Concepts

• Equivalent Fractions Property
  • If $a,b,c$ are whole numbers where $b\ne 0,c\ne 0$, then $\frac{a}{b}=\frac{a\cdot c}{b\cdot c}$ and $\frac{a\cdot c}{b\cdot c}=\frac{a}{b}$
• 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 $\frac{{a}^{m}}{{a}^{n}}={a}^{m-n},m>n$ and $\frac{{a}^{m}}{{a}^{n}}=\frac{1}{{a}^{n-m}},n>m$
• Quotient to a Power Property for Exponents
  • If $a$ and $b$ are real numbers, $b\ne 0$, and $m$ is a counting number, then ${\left(\frac{a}{b}\right)}^{m}=\frac{{a}^{m}}{{b}^{m}}$
  • 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 $1$.

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