Evaluate each exponential expression: (3^3)/(3^6)

Question

Accepted Answer

Hello everyone in this video we'll be practicing this operation where we have 25 to the fourth divided by five to the eighth. And we need to find a more simplified answer. So the first thing that I notice with this problem is that the bases are not the same. So on the numerator we have 25 as a base and on the denominator we have five as a base. So it's difficult to simplify because the bases are not the same. However if you recall that five times five is equal to 25 then we can try to convert the 25 in the numerator to a base five. So recall that five terms five is equal to 25 and five times five can also be expressed as five squared. So when I try to plug in five squared into the 25 to the fourth it becomes five squared With a four on the outside. And recall that when exponents are inside the parentheses we have to multiply so it becomes 52 times four and that becomes five to the eighth. So now I know that 25 to the fourth is equal to five to the eighth. So I can rewrite the expression 25 to the fourth divided by five to the eighth as five to the eighth over five to the eighth. And recall that anything over itself is equal to one. So that becomes our final answer and this aligns with sir choice. See hopefully this helps see you next time