Write Each of the Following in the Simplest Form: (A3)5 X A4

Write each of the following in the simplest form:
(a³)⁵ x a⁴

Sum

(a³)⁵ x a⁴
= (a)^3x5 x a⁴ .....(Using (a^m)ⁿ = a^mn)
= (a)¹⁵ x a⁴
= a^{15 +4} .....(Using a^m x aⁿ = a^{m +n})
= a¹⁹.

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Simplification of Expressions

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Chapter 6: Indices - Exercise 9.1

Chapter 6 Indices
Exercise 9.1 | Q 3.1

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 `

Simplify : `2[6 + 4 {"m"-6(7 - overline("n"+"p")) + "q"}]`

Simplify: (x⁵ ÷ x²) × y²× y³

Write each of the following in the simplest form:

`"a"^(1/3) ÷ "a"^(-2/3)`

Simplify the following:

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

Simplify the following:

`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`

Simplify the following:

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

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

Simplify the following:

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