Negative powers

A negative power indicates the reciprocal of the base. For a power of -1:

a^{-1}=\frac1a

For a negative power other than -1, it indicates the reciprocal of the fraction, but the order of the base remains. This can be shown as:

a^{-x}=\frac1{a^x}

Example: evaluate (\frac34)^{-1}

Example: evaluate (\frac73)^{-2}

flashcards

QuestionAnswer
a^{-1}same as \frac1a
What does a^{-x} equal?\frac1{a^x}
Evaluate (\frac{3}{4})^{-1}\frac{1}{\frac{3}{4}}=\frac{4}{3}
Evaluate (\frac{7}{3})^{-2}(\frac{3}{7})^{2}=\frac{9}{49}