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Simplify the Following and Express with Positive Index : (32)^(-2/5) ÷ (125)^(-2/5) - Mathematics

Sum

Simplify the following and express with positive index :
`(32)^(-2/5) ÷ (125)^(-2/5)`

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Solution

`(32)^(-2/5) ÷ (125)^(-2/5)`

= `[(32)^(-2/5)/(125)^(-2/3)]`

= `(125)^(2/3)/(32)^(2/5)`

= `( 5 xx 5 xx 5 )^(2/3)/( 2 xx 2 xx 2 xx 2 xx 2 )^(2/5)`

= `(5^3)^(2/3)/(2^5)^(2/5)`

= `5^2/2^2`

= `25/4`

= `6 1/4`

Concept: Laws of Exponents
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APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 4.3 | Page 98
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