Negative power — lesson. Mathematics CBSE, Class 7.

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Definition of degree if the magnifier is a negative integer

A fraction with a whole negative multiplier is taken to be a fraction with a numerator of \(1\), but the denominator is the same base with the opposite positive multiplier.

Example:

a^{- n} = \frac{1}{a^{n}} (n - natural numbers)

Exceptions are the degree of \(0\) with a negative multiplier,

0^{- 3}

and

0^{- 1}

3^{- 2} = \frac{1}{3^{2}} = \frac{1}{9}

10^{- 1} = \frac{1}{10^{1}} = \frac{1}{10} = 0. 1

{(- 4)}^{- 3} = \frac{1}{{(- 4)}^{3}} = \frac{1}{- 64} = - \frac{1}{64}

{(- 1)}^{- 3} = \frac{1}{{(- 1)}^{3}} = \frac{1}{- 1} = - 1

Important!

When increasing the share to a negative degree, the law shall be used:

{(\frac{a}{b})}^{- n} = {(\frac{b}{a})}^{n}

{(\frac{2}{3})}^{- 3} = {(\frac{3}{2})}^{3} = \frac{27}{8} = 3 \frac{3}{8}

Reference:

Mathematics Handbook for Students / J. Mencis, A. Sika - Riga: The Star, pp. 96 - 98, 1990

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6. Negative power

Theory: