`@` `\text {Ans}`
`\downarrow`
`a,`
`11*11*11*11*11 = 11^(1+1+1+1+1) = 11^5`
`b,`
`2*2*2*4 = 2*2*2* 2^2 = 2^(1+1+1+2) = 2^5`
`c,`
`x*x*x*x*x^2 = x^(1+1+1+1+2) = x^6`
`d,`
`45*20*30`
`= 3^2 * 5 * 2^2 * 5 * 5 * 3 * 2`
`= 3^3 * 5^3 * 2^3`
`= (3 * 5 * 2)^3`
`= 30^3`
`e,`
`2^5 * 2^3 \div 2^7`
`= 2^(5+3 - 7)`
`= 2^0 = 1`
`f,`
`a^(x+2) \div a^2`
`= a^(x + 2 - 2)`
`= a^x`
`g,`
`5^10 \div 5^3`
`= 5^(10 - 3)`
`= 5^7`
`h,`
`81 \div 3^2`
`= 3^4 \div 3^2`
`= 3^(4-2)`
`= 3^2`
a) \(11\cdot11\cdot11\cdot11\cdot11=11^5\)
b) \(2\cdot2\cdot2\cdot4=2\cdot2\cdot2\cdot2\cdot2=2^5\)
c) \(x\cdot x\cdot x\cdot x\cdot x^2=x^6\)
d) \(45\cdot20\cdot30=3^2\cdot5\cdot2^2\cdot5\cdot2\cdot3\cdot5=3^3\cdot5^3\cdot2^3=30^3\)
e) \(2^5\cdot2^3:2^7=2^8:2^7=2\)
f) \(a^{x+2}:a^2=a^x\cdot a^2:a^2=a^x\)
g) \(5^{10}:5^3=5^7\)
h) \(81:3^2=3^4:3^2=3^2\)
