Answer
$625$
Work Step by Step
In this problem, we can break big numbers down to be able to work with them with more ease. Let us break down the number $125$ to base $5$ raised to the $3rd$ power:
$(5^3)((5^3)^{1/3})$
Raising a power to a power means we can multiply the two exponents together, keeping the same base. Let's multiply the exponents together first:
$(5^3)(5^{(3)(1/3)})$
Multiply to simplify the exponents:
$(5^3)(5^{3/3})$
Reduce the fraction in the exponent by dividing both numerator and denominator by $3$, the greatest common factor:
$(5^3)(5^{1})$
When we multiply two exponents with the same base, we just add the two exponents, keeping the base:
$5^{3 + 1}$
Add the exponents:
$5^{4}$
Evaluate by raising $5$ to the power of $4$:
$625$
