`a)` `( 4^6 × 3^4 × 9^5 )/( 6^12 )`
`=` `(( 2 × 2 )^6 × 3^4 × ( 3^2 )^5)/((2^2 × 3)^12)`
`=` `( 2^6 × 2^6 × 2^5 × 3^4 × 3^5)/( 2^24 × 3^12 )`
`=` `( 2^(6 + 6 + 5) × 3^( 4 + 5))/( 2^24 × 3^12)`
`=` `( 2^17 × 3^9)/( 2^24 × 3^12)`
`=` `1/( 2^7 × 3^3 )`
`b)` `( 21^2 × 14 × 125 )/( 35^3 × 6 )`
`=` `((3 × 7)^2 × 2 × 7 × 5^3)/((5 × 7)^3 × 2 × 3)`
`=` `(3^2 × 7^2 × 7 × 2 × 5^3)/( 5^3 × 7^3 × 2 × 3)`
`=` `( 3 × 1 × 1 × 1 )/( 1 × 1 × 1 × 1 )`
`=` `3/1` `= 3`
`c)` `( 45^3 × 20^4 × 18^2)/( 180^5 )`
`=` `((5 × 3^2)^3 × (2^2 × 5)^4 × (2 × 3^2)^2)/((2^2 × 3^2 × 5)^5)`
`=` `(5^3 × 3^6 × 2^2 × 5^4 × 2^2 × 3^2)/( 2^10 × 3^10 × 5^5)`
`=` `( 5^9 × 3^7 × 2^4 × 5^4 )/( 2^10 × 3^10 × 5^5 )`
`=` `( 5^4 × 1 × 1 × 5^4 )/( 2^6 × 3^3 × 1)`
`=` `( 5^8)/( 2^6 × 3^3 )`
`d)` `( 2^13 + 2^5)/( 2^10 + 2^2)`
`=` `( 2^3 + 2^3)/( 1 × 1 )`
`=` `8 + 8`
`=` `16`
@ Rin
