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Question
`(0.000729)^((-3)/4) xx (0.09)^((-3)/4)` = ______
Options
`(10^3)/(3^3)`
`(10^5)/(3^5)`
`(10^2)/(3^2)`
`(10^6)/(3^6)`
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Solution
`(10^6)/(3^6)`
Explanation;
Hint:
`(0.000729)^((-3)/4) xx (0.09)^((-3)/4) = (0.000729 xx 0.09)^((-3)/4)`
= `(729 xx 10^(-6) xx 9 xx 10^(-2))^((-3)/4)`
= `[(9 xx 729) xx 10^(-8)]^((-3)/4)`
= `(3^8 xx 10^(-8))^((-3)/4)`
= `3^(8 xx (-3)/4) xx 10^(-8 xx (-3)/4)`
= 3−6 × 106
= `(10^6)/(3^6)`
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