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Question
Evaluate :
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
Solution
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`
= `5^(-4) xx ( 5 xx 5 xx 5 )^(5/3) ÷ ( 5 xx 5 )^(-1/2)`
= `5^(-4) xx ( 5^3 )^(5/3) ÷ ( 5^2 )^(-1/2)`
= `5^(-4) xx [( 5)^[3 xx 5/3]] ÷[ ( 5)^[2 xx -1/2]]`
= `[ 5^(-4) xx 5^(5)]/5^(-1)`
= `[5^( 5 - 4 )]/[5^(-1)]`
= `[5^1]/[5^-1]`
= `5^[ 1 - (- 1)]`
= `5^2`
= 5 x 5
=25
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