Simplify the expressions using the quotient to a power property. ( 8 11 ) 2 \left(\frac{8}{11}\right)^2

in some problems where you have quotients, it's perfectly okay to see quotients that don't involve variables at all and only just numbers all raised to exponents. So for example, we've got eight over 11, in parenthesis, all raised to the second power or you could say eight over 11 squared. We're gonna simplify this expression by using our power of quotient rule or sometimes called the quotient to a power property, just the same as we've done in other videos. Basic idea, we're gonna distribute this exponent to both the numerator and also the denominator and then we're going to simplify. So if we distribute the two to the eights in the numerator, we get eight squared and then in denominator, we get 11 squared. Now, if we only just had variables raised to exponents, we can't simplify this any further. But eight squared is an actual number. So we're going to go ahead and take one more step and actually just simplify this. We have no more exponents attached to numbers. So, what is eight squared? You just may remember this from your multiplication tables or your squares but eight squared is just eight times eight which is just 64. Now, 11 squared, just similarly, you can go ahead and work it out on the side or you may recognize this as a square is a 121. Now, we just have to ask ourselves, can we actually simplify this any further? The there is a bunch of factors of 64 but there actually only is two factors of a 121. It's prime so we can't actually factor that any further. So we really can't simplify this anymore and we have 64 over 121 as our final answer. Thanks for watching and see you next