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

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)`

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

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

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

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:
`x^("m" + 2"n"). x^(3"m" - 8"n") ÷ x^(5"m" - 60)`

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)`

Simplify the following:

`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`