# Negative exponent help. How to change a minus exponent into a fraction.

If you have a negative exponent then:

x-n = 1/xn

So all you have to do is to convert it to a fraction; where the top of the fraction is always equal to 1 and xn goes on the denominator of the fraction.

Example 1

Work out the value of 6⁻². Do not use a calculator.

Put 1 on the numerator of the fraction.

Put 6² on the denominator of the fraction.

Therefore, 6⁻² = 1/6² = 1/36 since 6² = 36.

So 6⁻² = 1/36

Example 2

Work out the value of 5⁻³. Do not use a calculator.

Put 1 on the numerator of the fraction.

Put 5³ on the denominator of the fraction.

Therefore, 5³ = 1/5³ = 1/125 since 5³ = 125

So 5⁻³ = 1/125

Example 3

Work out the value of 12⁻¹. Do not use a calculator.

Put 1 on the numerator of the fraction.

Put 12¹ on the denominator of the fractions.

Therefore, 12⁻¹ = 1/12¹ = 1/12 since 12¹ = 12.

So 12⁻¹ = 1/12

Example 4

Write 1/49 in the form x⁻² where x is a number to be found.

This time the question is asking you to apply the negative exponent law in reverse (opposite way to the first 3 examples).

Since 49 is equal to 7² then:

1/49 = 1/7²

So using the negative exponent rule then:

1/7² = 7⁻².

Therefore, the value of x is 7.

Example 5

Write 1/64 in the form y⁻³ where y is a number to be found.

This time the question is asking you to apply the negative exponent law in reverse (opposite way to the first 3 examples).

Since 64 can be written as 4³ then:

1/64 = 1/4³

So using the negative exponent rule then:

1/4³ = 4⁻³.

Therefore, the value of y is 4.

Example 6

Work out the value of (16/81)⁻².

This question is a little trickier. First of all (4/9)⁻² is the same as 4⁻²/9⁻².

Now if you use the negative exponent law on the numerator and denominator of the fraction you get:

4⁻²/9⁻² = (1/16)÷(1/81)

Now you can simplify this as you are dividing by a fraction (change the times to a divide and flip the second fraction over).

So 1/16 × 81/1 = 81/16 or 5 1/16.