MathematicsClass 8Exponents and Powers

Powers with Negative Exponents

Understanding how negative exponents represent the reciprocal of the base raised to a positive power.

Class 8 · MathematicsCBSE & ICSE SOF IMO

Definition

Powers with negative exponents represent the reciprocal of the base raised to the corresponding positive exponent. This concept allows us to write very small numbers compactly using negative indices. For any non-zero integer 'a' and integer 'n', a raised to the power of negative n is equal to 1 divided by a raised to the power of n.

Key formula

a^{-n} = \frac{1}{a^n}

Worked examples

Evaluate 2^{-3} to get \frac{1}{2^3} which equals \frac{1}{8}.

Simplify (\frac{2}{3})^{-2} by reciprocating the fraction to get (\frac{3}{2})^2, which equals \frac{9}{4}.

Express 5^{-1} as a fraction to get \frac{1}{5}.

Common mistakes

• Making the base negative instead of reciprocating it, such as writing 2^{-3} as -8.
• Forgetting to apply the exponent to both the numerator and denominator when dealing with fractions raised to a negative power.

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