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Question
Simplify:
`[(256"a"^16)/(81"b"^4)]^(-3/4)`
Solution
`[(256"a"^16)/(81"b"^4)]^(-3/4)`
`=[(4^4"a"^16)/(3^4"b"^4)]^(-3/4)`
`=(4^(4"x"-3/4)."a"^(16"x"-3/4))/(3^(4"x"-3/4)."b"^(4"x"-3/4)`
`=(4^-3."a"^-12)/(3^-3."b"^-3`
`=(3^3"b"^3)/(4^3"a"^12)` ...`(∵4^-3=1/4^3,1/3^-3=3^3, "a"^-12=1/"a"^12, 1/"b"^-3=b"^3)`
`=(27"b"^3)/(64"a"^12)`
`=27/64."a"^-12"b"^3`
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