Summary: Dividing Monomials

Key Concepts

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

Glossary

zero exponent

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

Licenses & Attributions