Question

Find the value of the following :
(i) $\frac{(7{)}^3\times 21}{3}$ (ii) $\frac{(121{)}^3\times 33}{3}$
(iii) $\frac{(169{)}^2}{{13}^2}$ (iv) $\frac{(2^{\circ }+3^{\circ })5^2}{25}$

Answer 1

(i) $\frac{(7{)}^3\times 21}{3}=7^3\times 7=7^{3+1}=7^4$

(ii) $\frac{(121{)}^3\times 33}{3}=({11}^2{)}^3\times 11={11}^6\times {11}^1={11}^7$

(iii) $\frac{(169{)}^2}{{13}^2}=\frac{\left[\right(13{)}^2{]}^2}{{13}^2}=\frac{{13}^4}{{13}^2}={13}^{4-2}={13}^2=169$

(iv) $\frac{(2^{\circ }+3^{\circ })5^2}{25}=\frac{(1+1){.5}^2}{5^2}=\frac{2}{5^{2-2}}=\frac{2}{5^0}=\frac{2}{1}=2$