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

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 6: Indices - Exercise 9.1

Chapter 6 Indices
Exercise 9.1 | Q 5.2

Solve : 3(2^x + 1) - 2^x+2 + 5 = 0.

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

Simplify : `2{m-3(n+overline(m-2n))}`

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

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

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

Write the following in the simplest form:
(b^-2 - a^-2) ÷ (b^-1 - a^-1)

Simplify the following:

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

Simplify the following:

`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`

Simplify the following:

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