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Calculating with Negative Indices

Calculating with Negative Indices

A negative index indicates that the value is a reciprocal of the number.

Write the number as a denominator, changing the negative index to a positive index. Set the numerator to 1.

For example, 2-2 can also be written as `frac(1)(2^2)` which evaluates to `frac(1)(4)`.

Example 1

Calculate 42 ÷ 26. Write the answer as a fraction.

Rewrite the question as (22)2 ÷ 26

Evaluate to 24 ÷ 26

= 2(4-6)

= 2-2

= `frac(1)(2^2)` = `frac(1)(4)`

Answer: `frac(1)(4)`

Example 2

Calculate 52 ÷ 5-2.

5(2 - -2) = 54.

Answer: 625

See also Multiplying and Dividing Power Terms