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

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

Simplify : a² − 2a + {5a² − (3a - 4a²)}

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

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

Simplify: x⁵ ÷ (x² × y²) × y³

Write the following in the simplest form:
(b^-2 - a^-2) ÷ (b^-1 - a^-1)

Simplify the following:

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

Simplify the following:

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

Simplify the following:

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

Simplify the following:

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