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)`

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

Simplify : `"p"^2"x"-2{"px"-3"x"("x"^2-overline(3"a"-"x"^2))}`

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

Simplify: x⁵ ÷ (x² × y²) × y³

Simplify: `3"a"xx[8"b" ÷ 4-6{"a"-(5"a"-overline(3"b"-2"a"))} ]`

Write each of the following in the simplest form:
(a³)⁵ x a⁴

Simplify the following:

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

Simplify the following:

`(27/343)^(2/3) ÷ (1)/(625/1296)^(1/4) xx (536)/root(3)(27)`

Simplify the following:

`(2^"m" xx 3 - 2^"m")/(2^("m" + 4) - 2^("m" + 1)`