Simplify the Following and Express with Positive Index: ( P − 3 ) 2 3 1 2 - Mathematics

Simplify the following and express with positive index:

`[("p"^-3)^(2/3)]^(1/2)`

Sum

`[("p"^-3)^(2/3)]^(1/2)`

= `"p"^(-3 xx 2/3 xx 1/2)` .....(Using (a^m)ⁿ = a^mn)
= p^-1
= `(1)/"p"`.

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Simplification of Expressions

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 5.2

Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`

If (a^m)ⁿ = a^m .aⁿ, find the value of : m(n - 1) - (n - 1)

Evaluate :
`[ 2^n xx 6^(m + 1 ) xx 10^( m - n ) xx 15^(m + n - 2)]/[4^m xx 3^(2m + n) xx 25^(m - 1)]`

Simplify : −3 (1 − x²) − 2{x² − (3 − 2x²)}

Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`

Simplify : `3"x"-[4"x"-overline(3"x"-5"y")-3 {2"x"-(3"x"-overline(2"x"-3"y"))}]`

Simplify: 7x + 4 {x² ÷ (5x ÷ 10)} − 3 {2 − x³ ÷ (3x² ÷ x)}

Simplify the following:

`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`

Simplify the following:

`{("a"^"m")^("m" - 1/"m")}^(1/("m" + 1)`

Simplify the following:

`(5^x xx 7 - 5^x)/(5^(x + 2) - 5^(x + 1)`