Fractions
The values are [tex]\frac{1}{4} , \frac{1}{8} , \frac{1}{81}[/tex]
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)
[tex]\frac{1}{a}[/tex] = [tex]a^{-1}[/tex]
so accordingly
a)
4^(-1) or [tex]4^{-1}[/tex] can be represented exponentially as ¼ .
⇒ [tex]\frac{1}{4}[/tex]
Part b)
2^(-3) or [tex]2^{-3}[/tex]
We can simplify the exponent so that the power should be equal to -1.
And, so [tex]2^{3}[/tex] = 8
So we can write the above the expression as 8^(-1) or [tex]8^{-1}[/tex]
So the fraction corresponding to it is [tex]\frac{1}{8}[/tex].
⇒ [tex]\frac{1}{8}[/tex]
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) = [tex]\frac{1}{81}[/tex]
So the fraction obtained is [tex]\frac{1}{81}[/tex].
⇒ [tex]\frac{1}{81}[/tex]
The values are [tex]\frac{1}{4} , \frac{1}{8} , \frac{1}{81}[/tex]
