Making sense of algebra

Question

Simplify (3125x³¹²⁵)^1/5

Answer 1

(3125x^3125)^1/5

= (3125^.2)(x^(3125)(.2))

= 5x^625

Answer 2

To simplify that expression, we need to apply the power of products rule of exponents, which states that

1. (ab)^x = a^x b^x

Therefore, we have:

1. (3125x³¹²⁵)^1/5 = 3125^1/5 • (x³¹²⁵)^1/5

We can use the power rule to simplify the second term, which states that (a^b)^c= a^bc.

1. (x³¹²⁵)^1/5 = x^3125•(1/5) = x⁶²⁵

All that's left is to simplify the first term, 3125^1/5, which is another way of saying the "fifth root of 3125", which just comes out to 5. Therefore, the simplest form of our expression is: 5x⁶²⁵