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Question
Simplify.
`(3^(-5) xx 10^(-5) xx 125)/(5^(-7) xx 6^(-5))`
Solution
`(3^(-5)xx10^(-5)xx125)/(5^(-7)xx6^(-5))`
`=(3^(-5)xx(2xx5)^5xx5^3)/(5^(-7)xx(2xx3)^(-5))`
`=((3)^(-5)xx(2)^(-5)xx(5)^(-5)xx(5)^3)/((5)^(-7)xx(2)^(-5)xx(3)^(-5))` ...[∵ (a × b)m = am × bm]
`= 3^(-5-(-5))xx2^(-5-(-5))xx5^(-5+3-(-7))` ...(am ÷ an = am−n)
= 30 × 20 × 55 ...(a0 = 1)
= 55
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