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)`

योग

`[("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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अध्याय 6: Indices - Exercise 9.1

अध्याय 6 Indices
Exercise 9.1 | Q 5.2

If 3^4x = ( 81 )^-1 and `10^(1/y) = 0.0001, "Find the value of " 2^(- x ) xx 16^y `

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

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

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

Simplify : a² − 2a + {5a² − (3a - 4a²)}

Simplify: (x⁵ ÷ x²) × y²× y³

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 xx^9)^(2/3)`

Simplify the following:

`((64"a"^12)/(27"b"^6))^(-2/3)`