Exponent and Powers Quiz

Simplify the expression: (3⁴ × 3⁵) ÷ 3²

1. 3⁷
2. 3⁹
3. 3⁸
4. 3⁶

Answer: (a) 3⁷

A star has a mass of 0.000027 solar masses.Express this mass in standard form. If this star's mass is multiplied by (3 × 10⁶), what will be its new mass in standard form?and calculate the difference between the new mass and the original mass in standard form.

1. 2.7 × 10⁻⁵, 81, 82
2. 2.7 × 10^(-5), 81, 80.999973
3. 2.7 × 10^(-6), 8.1 × 10^1, 81
4. 2.7 × 10^(-4), 8.1 × 10^2, 80.999973

Answer: (b) 2.7 × 10^(-5), 81, 80.999973

The mass of a bacteria cell is 0.00000000035 kg. Express this number in standard form.

1. 3.5 × 10⁻⁷ kg
2. 3.5 × 10⁻⁸ kg
3. 3.5 × 10⁻⁹ kg
4. 3.5 × 10⁻¹⁰ kg

Answer: (d) 3.5 × 10⁻¹⁰ kg

If a = 2³ and b = 2⁴, what is the value of (a × b²) ÷ b?

1. 2⁵
2. 2⁶
3. 2⁷
4. 2⁴

Answer: (c) 2⁷

A mathematician is exploring the properties of fractional bases and negative exponents. She encounters the following expression. Evaluate it. (1/4)⁻² × (1/16)¹/²

1. 1
2. 4
3. 1/4
4. 16

Answer: (b) 4

Which of the following is equal to (4 × 10²) ÷ (2 × 10⁻³)?

1. 2 × 10⁴
2. 2 × 10⁶
3. 2 × 10⁵
4. 2 × 10³

Answer: (c) 2 × 10⁵

Multiply 4.1 × 10⁻³ and 2.5 × 10⁴ and express the product in standard form.

1. 1.025 × 10⁶
2. 1.025 × 10⁴
3. 1.025 × 10⁻²
4. 10.25 × 10¹

Answer: (d) 10.25 × 10¹

A scientist is analysing the concentration of a chemical in a solution. The measurements are as follows: The first measurement is 0.00000756 litres. The second measurement is 3 × 10² litres. Express the first measurement in standard form. Multiply the result from step 1 with the second measurement. Provide the final answer in both standard form and usual form, with clear calculations..

1. 2.268 × 10⁻³, Usual form: 0.002268
2. 2.268 × 10⁻⁶, Usual form: 0.000002268
3. 2.268 × 10⁻⁵, Usual form: 0.00002268
4. 2.268 × 10⁻², Usual form: 0.02268

The number 7,650 is given. Find the square of this number.

1. 5.85225 × 10⁷
2. 5.85 × 10⁷
3. 5.5225 × 10⁷
4. 58.5225 × 10⁶

Answer: (a) 5.85225 × 10⁷

A virus has a mass of 1.6 × 10⁻¹⁹ g. What is the total mass of 5 × 10⁷ viruses? Express in standard form.

1. 8 × 10⁻¹² g
2. 8 × 10⁻¹⁵ g
3. 8 × 10⁻¹³ g
4. 8 × 10⁻¹⁴ g

Answer: (a) 8 × 10⁻¹² g