Question

How can you use the fact that 25^2=625 to show that 5^-4 =1/625 ? Explain your process thinking.

Answer 1

The answer to your question is:

Explanation:

Given

25² = 625

Show that

5⁻⁴ =
`(1)/(625)`

Process

Find the prime factors of 25

25 5

5 5

1

Then 25 = 5²

Substitution

(5²)² = 625

(5)⁴ = 625

Get the inverse

(5⁴) ⁻¹ = 625⁻¹

But negative powers are not allowed, then,

`5^(-4) = (1)/(5^(4) ) = (1)/(625)`