Exponents and Powers quiz

The value of 3^4 is:

In 5^3, the base is:

a^m x a^n equals:

The value of 1000^0 is:

(-1)^51 equals:

The standard form of 45,000 is:

(2^3)^2 equals:

625 written as a power of 5 is:

2^3 x 5^3 equals:

Which is greater?

Find the value of (-4)^3 and (-4)^2. (2 marks)

Express 10,000 as a power of 10 and 1,00,00,000 as a power of 10. (2 marks)

Simplify 2^10 / 2^7 and give the value. (2 marks)

Express 72 as a product of powers of prime factors. (2 marks)

Simplify (a^4)^3 x a^2. (2 marks)

Is 3^2 x 3^3 = 9^5? Explain. (2 marks)

Find the value of (2/3)^3. (2 marks)

Write 6.02 x 10^5 in usual form. (2 marks)

Which is greater: 2^10 or 10^2? Show working. (2 marks)

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

Find the value of (3^0 + 2^0) x 5^0 and of 2^0 + 3^0 + 4^0 + 5^0. Also find 1^100 + 0^100. (3 marks)

Simplify (4^3 x 4^5) / 4^6 and (5^2 x 5^4) / (5^3) and find the values. (3 marks)

Write in standard form: (i) 1,40,00,000 (ii) 3,00,000 (iii) 8,900,000. (3 marks)

Find x: (i) 2^x = 64 (ii) 3^x x 3^2 = 3^7 (iii) (5^2)^x = 5^8. (3 marks)

Simplify (2^4 x 3^2) / (6^2) and express 1,08,000 as a product of powers of prime factors. (3 marks)

Read the passage and answer the questions. The speed of light in vacuum is about 300,000,000 m/s. The distance of the Sun from the Earth is about 149,600,000,000 m. (i) Write the speed of light in standard form. (ii) Write the distance of the Sun in standard form. (iii) Which number has the larger power of 10? (5 marks)

Read the passage and answer the questions. A bacterium doubles every hour. A lab starts with 1 bacterium at 9 am. (i) How many bacteria are there at 1 pm? Write it as a power of 2. (ii) After how many hours will there be 1024 bacteria? (iii) Write the number after 10 hours using exponents. (5 marks)

Read the passage and answer the questions. Sana sends a message to 3 friends. Each of them forwards it to 3 new friends, and so on, each round. (i) How many new people receive it in round 4? Write as a power of 3. (ii) Find the value. (iii) In which round will 243 new people receive it? (5 marks)

Read the passage and answer the questions. A cube-shaped box has each side 10 cm. The volume of a cube is side x side x side. (i) Write the volume as a power of 10. (ii) If the side becomes 20 cm, write the volume as a product of powers of 2 and 10. (iii) How many times does the volume increase? (5 marks)

Read the passage and answer the questions. The population of India in 2011 was about 1,210,000,000. A small town has 1,21,000 people. (i) Write India's population in standard form. (ii) Write the town's population in standard form. (iii) How many times larger is India's population than the town's? Write as a power of 10. (5 marks)

State all six laws of exponents with one numerical example each. Then simplify (3^7 x 3^3) / (3^4)^2. (6 marks)

Draw factor trees for 432 and 3600. Express each as a product of powers of prime factors. (6 marks)

Simplify: (i) (2^8 / 2^5)^2 x 2^3 (ii) (6^2 x 6^4) / 6^3 (iii) (a^5 / a^3) x a^8 (iv) 4^5 / 4^3 x 4^0 (v) (3^2)^2 x 3^0. (6 marks)

Draw a place value chart for 7,05,32,904 and write the number in expanded form using powers of 10. Also write it in standard form, rounded to two decimal places. (6 marks)

Explain with examples why (-1)^n is 1 when n is even and -1 when n is odd. Then find (-1)^10 x (-1)^7, (-2)^3 x (-2)^2 and (-5)^3 / (-5)^2. (6 marks)