Question

Simplify $\frac{8^4\times {14}^3\times 5\times 3^4}{4^5\times 7^3\times 6^2}$ [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

Consider,

$\frac{8^4\times {14}^3\times 5\times 3^4}{4^5\times 7^3\times 6^2}$

$8^4=(2^3{)}^4=2^{12}$

${14}^3=(2\times 7{)}^3=2^3\times 7^3$

$4^5=(2^2{)}^5=2^{10}$

$6^2=(2\times 3{)}^2=2^2\times 3^2$

Substituting we get

$\frac{2^{12}\times 2^3\times 7^3\times 5\times 3^4}{2^{10}\times 7^3\times 2^2\times 3^2}$

$=2^{12+3-10-2}\times 7^{3-3}\times 5\times 3^{4-2}$

$=2^3\times 5\times 3^2$ [$\because a^0=1$]

$=8\times 5\times 9$

$=360$