Write Each of the Following in the Simplest Form: A-3 X A2 X A0 - Mathematics

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

Sum

a^-3x a² x a⁰
= `"a"^(-3+2+0)` ......(Using a^m x aⁿ = a^m+n)
= a^-1
= `(1)/"a"`.

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Simplification of Expressions

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 3.4

Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`

Solve for x : (13)^√x = 4⁴ - 3⁴ - 6

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

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

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

Simplify the following and express with positive index:

`[("p"^-3)^(2/3)]^(1/2)`

Simplify the following:

`(27 xx^9)^(2/3)`

Simplify the following:

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

Simplify the following:

`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`

Simplify the following:

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