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

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`

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

Simplify: a⁵ ÷ a³+ 3a × 2a

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

Simplify the following:

`((36"m"^-4)/(49"n"^-2))^(-3/2)`

Simplify the following:

`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`

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

Simplify the following:

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