Exponents and Powers quiz

The value of 2^-3 is:

The value of (-1)^-5 is:

For a non-zero x, x^m x x^n is equal to:

The standard form of 0.000035 is:

The value of 5^0 + 3^0 is:

The value of (1/3)^-2 is:

10^-2 is equal to:

The multiplicative inverse of 10^-100 is:

(2^3)^-2 is equal to:

The speed of light in vacuum written in standard form is:

Express 1/1000 and 1/64 as powers with negative exponents. (2 marks)

Evaluate (5/8)^-7 x (8/5)^-4. (2 marks)

Simplify (25 x t^-4) / (5^-3 x 10 x t^-8), where t is not zero. (2 marks)

Find the value of (3^0 + 4^-1) x 2^2. (2 marks)

Express 0.0000046 and 150000000000 in standard form. (2 marks)

Write 7.5 x 10^-5 and 1.0001 x 10^9 in usual form. (2 marks)

Evaluate (-2)^-3 and (-2)^-4. Explain why one is negative and the other positive. (2 marks)

How many times is 2.7 x 10^12 greater than 1.5 x 10^8? (2 marks)

Find x if 3^x = 1/81. (2 marks)

Simplify (-3)^4 x (5/3)^4. (2 marks)

Simplify: (i) (3^-7 / 3^-10) x 3^-5 (ii) ((1/2)^-1 - (1/4)^-1)^-1 (iii) (-2)^3 x (-2)^-6. (3 marks)

Find m so that (2/9)^3 x (2/9)^-6 = (2/9)^(2m-1). Also find n if 2^n x 2^3 = 2^-2. (3 marks)

The mass of the Earth is 5.97 x 10^24 kg and the mass of the Moon is 7.35 x 10^22 kg. Find their total mass and express it in standard form. About how many times heavier is the Earth than the Moon? (3 marks)

The distance of the Sun from the Earth is about 1.496 x 10^11 m and light travels at 3 x 10^8 m/s. Find the time taken by sunlight to reach the Earth, in seconds and in minutes (to one decimal place). (3 marks)

The size of a plant cell is 0.00001275 m and the diameter of a red blood cell is 0.000007 m. Write both in standard form and find how many times larger the plant cell is (to two decimal places). (3 marks)

Read the passage and answer the questions. The average distance of the Moon from the Earth is 3.84 x 10^8 m. Light travels at 3 x 10^8 m/s, so a signal sent from the Earth reaches the Moon in a very short time. (i) How long does light take to travel from the Moon to the Earth? (ii) Write the distance 3.84 x 10^8 m in usual form. (iii) Express this distance in kilometres in standard form. (5 marks)

Read the passage and answer the questions. Under an electron microscope, a virus particle has a diameter of about 0.0000001 m, while a bacterium of the type E. coli is about 0.000002 m long. (i) Write both sizes in standard form. (ii) How many times longer is the bacterium than the diameter of the virus? (iii) How many such virus particles placed side by side would cover 1 mm? (5 marks)

Read the passage and answer the questions. In computers, 1 kilobyte (KB) = 2^10 bytes, 1 megabyte (MB) = 2^20 bytes and 1 gigabyte (GB) = 2^30 bytes. (i) How many kilobytes make 1 MB? Use the laws of exponents. (ii) How many megabytes make 1 GB? (iii) Express the capacity of a 4 GB pen drive in bytes as a power of 2. (5 marks)

Read the passage and answer the questions. In a laboratory, a culture begins with one bacterium, and the number of bacteria doubles every 20 minutes. (i) How many bacteria will there be after 3 hours? Write your answer as a power of 2 and in usual form. (ii) After how many doublings will the number first exceed 1000? (iii) If there were 2^12 bacteria at noon, how many were there 40 minutes earlier? Write it using a negative exponent and as a power of 2. (5 marks)

Read the passage and answer the questions. A ream of paper contains 500 sheets and its thickness is 5 cm. (i) Find the thickness of one sheet in centimetres in standard form. (ii) Express this thickness in metres in standard form. (iii) How many sheets would be needed to make a stack 1 m high? (5 marks)

State the laws of exponents for a non-zero base and integer exponents, with one numerical example of each. Use them to simplify (i) (2^5 / 2^8)^5 x 2^-5 (ii) (-1/4)^-3 x (4/3)^-2. Write each answer as a fraction or integer. (6 marks)

Draw a powers-of-ten ladder from 10^-6 m to 10^12 m. Place on it, in standard form, the diameter of a red blood cell (0.000007 m), the thickness of a human hair (about 0.0001 m), the height of the Qutub Minar (72.5 m), the diameter of the Earth (12756000 m) and the distance from the Earth to the Sun (149600000000 m). Explain how standard form makes such comparisons easier. (6 marks)

Draw a pattern chart for powers of 3 from 3^3 = 27 down to 3^-2, dividing by 3 at each step. Use it to explain why x^0 = 1 and x^-m = 1/x^m. Then evaluate (i) 2^-1 + 3^-1 + 4^-1 (ii) (3^-1 + 4^-1 + 5^-1)^0. (6 marks)

Explain how writing numbers in standard form helps us compare very large and very small quantities. (i) The diameter of the Sun is 1.4 x 10^9 m and that of the Earth is 1.2756 x 10^7 m; compare them. (ii) Arrange in ascending order: 3.5 x 10^-4, 2.1 x 10^-6, 7 x 10^-5, 1.2 x 10^-3. (6 marks)

Simplify, showing every law used: (i) (3^-5 x 10^-5 x 125) / (5^-7 x 6^-5) (ii) (6^-1 - 8^-1)^-1 + (2^-1 - 3^-1)^-1 (iii) (2^0 + 3^-1) x 3^2. (6 marks)