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.

More by this Author


Comments

No comments yet.

    0 of 8192 characters used
    Post Comment

    No HTML is allowed in comments, but URLs will be hyperlinked. Comments are not for promoting your articles or other sites.


    Click to Rate This Article
    working