a) \(4^{10}\cdot8^{15}\)
\(=\left(2^2\right)^{10}\cdot\left(2^3\right)^{15}\)
\(=2^{20}\cdot2^{45}\)
\(=2^{65}\)
b) \(27^{16}:9^{10}\)
\(=\left(3^3\right)^{16}:\left(3^2\right)^{10}\)
\(=3^{48}:3^{20}\)
\(=3^{28}\)
c) \(\dfrac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^{10}\cdot\left(11+5\right)}{3^9\cdot16}\)
\(=\dfrac{3^{10}\cdot16}{3^9\cdot16}\)
\(=\dfrac{3}{1}\)
\(=3\)
`@` `\text {Ans}`
`\downarrow`
`a)`
`4^10 * 8^15`
`= (2^2)^10 * (2^3)^15`
`= 2^20 * 2^45`
`= 2^65`
`b)`
`27^16 \div 9^10`
`= (3^3)^16 \div (3^2)^10`
`= 3^48 \div 3^20`
`= 3^28`
`c)`
`(3^10*11 + 3^10*5)/(3^9 * 2^4)`
`= (3^10* (11+5))/(3^9*2^4)`
`= (3*16)/2^4 = 3/1=3`
