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 9: Indices - Exercise 9.1

Chapter 9 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 `[ 9^n. 3^2 . 3^n - (27)^n]/[ (3^m . 2 )^3 ] = 3^-3`

Show that : m - n = 1.

Evaluate : `((x^q)/(x^r))^(1/(qr)) xx ((x^r)/(x^p))^(1/(rp)) xx ((x^p)/(x^q))^(1/(pq))`

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

Simplify : `"p"^2"x"-2{"px"-3"x"("x"^2-overline(3"a"-"x"^2))}`

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

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

Simplify the following:

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

Simplify the following:

`(5^x xx 7 - 5^x)/(5^(x + 2) - 5^(x + 1)`

Simplify the following:

`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`