Question

Find the values of the following, giving your answers as fractions

4^(-1)
2^(-3)
3^(-4)

Answer 1

Fractions

The values are
`(1)/(4) , (1)/(8) , (1)/(81)`

Explanation:

As we know the fractions whose numerators are 1 can be represented in exponents and vice versa provided that the power of the exponent is (-1) ,

like 1/a = a^(-1)

`(1)/(a)` =
`a^(-1)`

so accordingly

a)

4^(-1) or
`4^(-1)` can be represented exponentially as ¼ .

⇒
`(1)/(4)`

Part b)

2^(-3) or
`2^(-3)`

We can simplify the exponent so that the power should be equal to -1.

And, so
`2^(3)` = 8

So we can write the above the expression as 8^(-1) or
`8^(-1)`

So the fraction corresponding to it is
`(1)/(8)`.

⇒
`(1)/(8)`

Part c)

3^(-4) now we can simplify the exponent so that the power of the exponent is -1.

And thus , (3 ^4)^(-1) = 81^(-1) =
`(1)/(81)`

So the fraction obtained is
`(1)/(81)`.

⇒
`(1)/(81)`

The values are
`(1)/(4) , (1)/(8) , (1)/(81)`