Evaluate each exponential expression: 5^(-3) • 5

Question

Accepted Answer

Hello. Everyone in this video we'll be evaluating this expression 11 to the negative 4th times 11. And In order to do this we want to remember that any number is to the power of one. Even if that exponent isn't explicitly written out. For example seven is the same as seven to the one power or seven to the first power because if we had 7 to 0 then that would be one. Remember that any integer to the power of zero becomes one. So if we recall that rule then we can look at the problem 11 to the negative fourth times 11 to 1. And we can see that they both have the same base of 11. So they're easier to combine looking at their exponents. And when we combine exponents with the same base we're going to be adding their exponents together. So 11 to the negative fourth plus one Simplifies to 11 to the negative third. So now we have 11 to the negative third. And we're going to want to recall that an exponent to the negative power can be expressed in the denominator for example seven to the negative one can be expressed as 1/7. So we're going to apply that to 11 to the negative third where we have 1/11 to the third. Notice how the negative on the three went away because now we're expressing it in the denominator and when we carry out this multiplication we get one divided by 1331. So this becomes our evaluation for the expression and this aligns with answer choice B. Hopefully this video helped see you next time.