Question

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

Answer 1

Answer:

The answer to your question is:

Step-by-step explanation:

Given

                                      25² = 625

Show that

                                     5⁻⁴ = $\frac{1}{625}$

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,

                                   $5^{-4} = \frac{1}{5^{4} } = \frac{1}{625}$