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

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 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 3.1

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

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

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

Simplify : `3"x"-[4"x"-overline(3"x"-5"y")-3 {2"x"-(3"x"-overline(2"x"-3"y"))}]`

Simplify the following and express with positive index:
3p^-2q³ ÷ 2p³q^-2

Simplify the following and express with positive index:

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

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:

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

Simplify the following:

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