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

Prove that : `( a + b + c )/( a^-1b^-1 + b^-1c^-1 + c^-1a^-1 ) = abc`

Prove that: `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^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

Write each of the following in the simplest form:
a² x a³ ÷ a⁴

Write each of the following in the simplest form:
a^-3x a² x a⁰

Simplify the following:

`(8 xx^6y^3)^(2/3)`

Simplify the following:

`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`

Simplify the following:

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

Simplify the following:

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