Question Video: Evaluating an Expression with an Integer Base and a Positive Rational Exponent Mathematics

Evaluate 3125^(3/5).


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.

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