Indices, Standard Form and Surds INSTRUCTIONS

1

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Indices, Standard Form and Surds

INSTRUCTIONS

● Read each problem below carefully, and answer them on a clean piece of paper.

● Show your complete work in an organised manner, then box your final answer.

1. Given that

(√𝑎 16

3 4

)(𝑏⁻ 2 3)

√(𝑎²)⁵ . 𝑏²

6 = 𝑎^𝑥𝑏^𝑦.

Hence, find the value of 𝑥 and the value of 𝑦.

2. Solve the following equations : (a) 32^𝑥+1. 8^𝑥 = ¹

2

(b) 4^𝑥+1 = √^82−𝑥

2^2𝑥+1 3

Mathematics Department

2 3. Simplify

2 𝑎−2+ ²

𝑏−2

√𝑎⁴+ √ ¹ 𝑏−6 3

4. Evaluate each of the following using a calculator and leave your answers in standard form correct to 3 significant figures.

(a) 12. 5 × 10⁷− 9.2 × 10⁵

(b) (3.2 × 10¹⁵) × (5 × 10⁻⁸)

(c) 10. 5 × 10⁻⁷ − 9.2 × 10⁻⁵

(b) ^3.2×10

5 5×10⁻⁸

3

5. Express ^2√5−√7

3√5+2√7 in the form of ^{𝑝−𝑞√35}

𝑟 where 𝑝, 𝑞, and 𝑟 are integers.

6. It is given the first three terms are

5

2√2+√3, − ³

√2+√3, − ⁴³

4√2+5√3.

Show that the sequence can be expresses as:

2√2 − √3, 3√2 − 3√3, 4√2 − 5√3

7. Given that 𝑎 =⁵

6, 𝑏 = 0.6666 …, and

𝑥 = 256.

Hence, find the value of (^𝑥𝑎

𝑥^𝑏)^𝑎+𝑏.