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

If you have a negative exponent then:

**x ^{-n} = 1/x^{n}**

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 x^{n} 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.

## More by this Author

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 26
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...

## Comments

No comments yet.