Class Test: Exponents and Surds

About this video

A Grade 11 class test on exponents and surds, answered step by step: exponential equations by a common factor and by the k-method, expanding a surd bracket properly, simplifying with a common factor, and why you cannot take the root of each term separately.

What it covers

• Exponential equations: a common factor, or the k-method
• Squaring a two-term bracket: write it twice and FOIL
• Simplifying surds: √27 = 3√3
• Splitting the exponents to take out a common factor
• A difference of squares under a root

Exercises to try

Work each one out, then click to reveal the answer.

1. 1

   Solve 2^{2x + 1} + 2^2x = 24.

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   2^2x(2 + 1) = 24 → 2^2x = 8 = 2³ → x = 3/2
2. 2

   Solve 9^x − 10 · 3^x + 9 = 0.

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   Let 3^x = k: k² − 10k + 9 = 0 → (k − 1)(k − 9) = 0 → x = 0 or x = 2
3. 3

   Simplify √50 + √18.

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   5√2 + 3√2 = 8√2
4. 4

   Expand (2√3 − 1)(√3 + 4).

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   6 + 8√3 − √3 − 4 = 2 + 7√3
5. 5

   Simplify (2^{x + 2} − 2^x)/(3 · 2^x).

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   (2^x(4 − 1))/(3 · 2^x) = 1