Question

Simplify and reduce. show the work. ^= an exponent of 2 and 0
(-2 3/4 + 1 2/3)^2 - (-7/9)^0

Answer 1

first off, let's convert the "mixed" fractions to "improper", and take it from there. Keeping in mind that anything(except 0 itself) raised at 0, is 1. Also recall that minus times minus is plus.


`\bf \stackrel{mixed}{-2(3)/(4)}\implies -\cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{-\cfrac{11}{4}}\\\\\\ \stackrel{mixed}{1(2)/(3)}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}\\\\ -------------------------------\\\\`


`\bf \left( -2(3)/(4) \right)^2-\left( 1(2)/(3) \right)^0\implies \left(-\cfrac{11}{4} \right)^2-\left( \cfrac{5}{3} \right)^0\implies \left(-\cfrac{11}{4} \right)\left(-\cfrac{11}{4} \right)~-~1 \\\\\\ \left(\cfrac{11}{4} \right)\left(\cfrac{11}{4} \right)-1\implies \left(\cfrac{11}{4} \right)^2-1\implies \cfrac{11^2}{4^2}-1\implies \cfrac{121}{8}-1 \\\\\\ \cfrac{121-8}{8}\implies \cfrac{113}{8}\implies 14(1)/(8)`