CLASS 8 · FREE LEARNING CORNER

Powers, equations & proportional thinking

Strengthen the ideas that connect middle-school maths with higher classes.

Try the 5-question check Read the example & worksheet ↓

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Five questions. No timer, no registration. Keep a notebook nearby and show your working. This is a small practice snapshot, not a full assessment or rank prediction.

CLASS 8 · SAMPLE MODULE

Understand. Work it out. Check.

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One idea to remember

For the same non-zero base a, aᵐ × aⁿ = aᵐ⁺ⁿ and aᵐ ÷ aⁿ = aᵐ⁻ⁿ. These rules follow by counting repeated factors, not by adding or dividing the bases.

Worked example: Simplify 2³ × 2².

2³ means three factors of 2; 2² means two factors of 2.
Together there are five factors: 2 × 2 × 2 × 2 × 2.
So 2³ × 2² = 2⁵ = 32.

Your turn

Write your method before opening the answer. These original questions are for practice, not official past-exam papers.

1. Solve 2x + 5 = 3x − 4.

Show answer & explanation

Subtract 2x: 5 = x − 4. Add 4 to both sides: x = 9.

2. Simplify 5⁶ ÷ 5².

Show answer & explanation

5⁴

Cancel two factors of 5 from numerator and denominator. Four remain: 5⁶⁻² = 5⁴.

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