Question

45¹⁰.5²⁰/75¹⁵

Answer 1

\(\frac{45^{10}.5^{20}}{75^{15}}=\frac{\left(3^2.5\right)^{10}.5^{20}}{\left(3.5^2\right)^{15}}=\frac{3^{20}.5^{10}.5^{20}}{3^{15}.5^{30}}\)

                   \(=\frac{3^{20}.5^{30}}{3^{15}.5^{30}}=\frac{3^5.1}{1.1}=3^5=243\)

Answer 2

\(\frac{45^{10}\cdot5^{20}}{75^{15}}=\frac{3^{20}\cdot5^{30}}{3^{15}\cdot5^{30}}=3^5=243\)

Answer 3

\(\frac{45^{10}\cdot5^{20}}{75^{15}}\)

\(=\frac{\left(9\cdot5\right)^{10}\cdot5^{20}}{\left(3\cdot5\cdot5\right)^{15}}\)

\(=\frac{9^{10}\cdot5^{10}\cdot5^{20}}{3^{15}\cdot5^{15}\cdot5^{15}}\)

\(=\frac{\left(3^2\right)^{10}\cdot5^{30}}{3^{15}\cdot5^{30}}\)

\(=\frac{3^{20}\cdot5^{30}}{3^{15}\cdot5^{30}}\)

\(=3^5\)

\(=243\)