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 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 5.2

Solve for x : (13)^√x = 4⁴ - 3⁴ - 6

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)

Evaluate : `((x^q)/(x^r))^(1/(qr)) xx ((x^r)/(x^p))^(1/(rp)) xx ((x^p)/(x^q))^(1/(pq))`

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

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

Simplify : `"a"-["a"-overline("b+a") - {"a"-("a"- overline("b"-"a"))}]`

Simplify: a⁵ ÷ a³+ 3a × 2a

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

Simplify the following:

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