AC9M9A01Year 9AlgebraPractised on site

AC9M9A01 — Year 9 Algebra

Official Curriculum Content Description:

apply the exponent laws to numerical expressions with integer exponents and extend to variables

Worked Examples (1)

Example 1Index Laws with Algebraic Variables

Simplify

\frac{x^{-2}}{x^{-5}}

to the form

x^n

. What is the value of the exponent

n

Common mistake: Adding exponents when dividing terms instead of subtracting.

Correct Answer:

3

Worked Solution:

1. Apply the quotient law of exponents:

\frac{x^a}{x^b} = x^{a-b}

. 2. Subtract the bottom exponent from the top exponent:

(-2) - (-5) = 3

. 3. Therefore,

\frac{x^{-2}}{x^{-5}} = x^{3}

, so

n = 3

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