One of the my best mistakes I made this week was when I was answering a question with a decimal radicand and decimal exponent. The question I’m referring to is…

The biggest mistake I made while solving that was solving it with decimals and lets just say I was on the question for around 10 minutes, now lets show the way I learned that made me realize that I was just complicating it for myself and making it harder on myself…

The first thing I did was to make both decimals into fractions and I already know that 0.81 into a fraction is just 81/100 and -1.5 as a fraction is -3/2.

Now that I have the fractions, I know that when I have an exponent as a fraction, then the denominator is going to be what I root the number by and the numerator of the exponent is going to stay as a power with the base, which gives me √81/100 with a -3 exponent, and since I know that when square rooting a fraction, you are simply just square rooting both the top and the bottom of the fraction, and the same applies to the exponent when it’s outside a bracketed number which means it applies to all the numbers in the fraction.

since I know that the square root of both 81 and 100 is 9 and 10, I’m left with 9/10 with -3 exponents on both top and bottom, since I know you can’t just have a negative exponent on a base and I got to make it positive, the way to do that is to reciprocate the fraction which mean flip it around so the numerator is now the denominator and vice versa, so now I’m left 10/9 with a positive 3 as an exponent.

Now that I’m left with a fraction with positive exponents, all I have to do is cube both the top and bottom which means multiply them by themselves 3 times, ex. 9x9x9 and 10x10x10. After, now I am left with my final answer of 1000/729.