Write Each of the Following in the Simplest Form: A2 X A3 ÷ A4

Write each of the following in the simplest form:
a² x a³ ÷ a⁴

Sum

a² x a³ ÷ a⁴
= `"a"^(2+3 - 4)` .....(Using a^m x aⁿ = a^{m + n} and a^m ÷ aⁿ = a^{m - n})
= a¹
= a.

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Simplification of Expressions

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Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 3.2

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

Show that : m - n = 1.

Prove that: `a^-1/(a^-1+b^-1) + a^-1/(a^-1 - b^-1) = (2b^2)/(b^2 - a^2 )`

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

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

Simplify : `2{m-3(n+overline(m-2n))}`

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

Simplify the following:

`((64"a"^12)/(27"b"^6))^(-2/3)`

Simplify the following:

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