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Evaluate : 5^(-4) X ( 125)^(5/3) ÷ (25)^(-1/2) - Mathematics

Sum

Evaluate :
`5^(-4) xx ( 125)^(5/3) ÷ (25)^(-1/2)`

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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

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 1.2 | Page 98
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