Video Transcript
Evaluate 3125 to the power
three-fifths.
To answer this question, we’re
going to use the rule that 𝑥 to the power of 𝑎 over 𝑏 is equivalent to the 𝑏th
root of 𝑥 to the power of 𝑎. So in a fractional exponent, the
top number is the power. So here we’ll be taking the third
power. And the denominator is the root, so
here we’ll be finding the fifth root.
So we start by taking the fifth
root of 3125, and then we find the third power of that. Starting with the fifth root of
3125, that’s equal to five, because five times five times five times five times five
is 3125. And we’ll then take the third power
of five, which means that we’re working out five times five times five. And five times five is 25, times
five will give us 125. So 3125 to the power of
three-fifths is 125.
