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]{\Large\frac{a}{b}}={\Large\frac{a\cdot c}{b\cdot c}}[/latex] and [latex]{\Large\frac{a\cdot c}{b\cdot c}}={\Large\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]{\Large\frac{{a}^{m}}{{a}^{n}}}={a}^{m-n},m>n[/latex] and [latex]{\Large\frac{{a}^{m}}{{a}^{n}}}={\Large\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]{\Large{\left(\frac{a}{b}\right)}}^{m}={\Large\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].