Question

Find the values of the following, giving your answers as fractions 4^(-1) 2^(-3) 3^(-4)

Answer 1

Fractions

The values are  $\frac{1}{4} , \frac{1}{8} , \frac{1}{81}$

Step-by-step 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)  

$\frac{1}{a}$  = $a^{-1}$

so accordingly

a)

   4^(-1) or $4^{-1}$ can be represented exponentially as ¼ .

⇒   $\frac{1}{4}$

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 $\frac{1}{8}$.

⇒ $\frac{1}{8}$

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)  = $\frac{1}{81}$

So the fraction obtained is $\frac{1}{81}$.

⇒ $\frac{1}{81}$

The values are  $\frac{1}{4} , \frac{1}{8} , \frac{1}{81}$