Powers and Exponents

Math ⇒ Number and Operations

Powers and Exponents starts at 6 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Powers and Exponents. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 10

A scientist writes the number 3,200,000 as 3.2 × 10ⁿ. What is the value of n?

Explain the difference between a negative exponent and a positive exponent.

Explain why 0⁰ is considered undefined.

If 2^x = 16, what is the value of x?

If 3^x = 81, what is the value of x?

If a^m × aⁿ = a^k, what is the value of k in terms of m and n?

A scientist writes the number 3,200,000 as 3.2 × 10ⁿ. What is the value of n?

A population of bacteria triples every hour. If the initial population is P, express the population after n hours as a power of 3.

If aⁿ = 1, which of the following must be true? (1) a = 1 for any n (2) n = 0 for any a ≠ 0 (3) a = 0 for any n (4) n = 1 for any a

Which of the following is equal to 10^-2? (1) 100 (2) 0.01 (3) -100 (4) 0.1

Which of the following is equal to 5⁰? (1) 0 (2) 1 (3) 5 (4) Undefined

Which of the following is the correct value of (−1)¹⁰⁰? (1) 1 (2) −1 (3) 0 (4) 100

Fill in the blank: (a⁵ × a³) ÷ a⁴ = a^______

Fill in the blank: 10³ × 10⁻⁵ = 10^______

Fill in the blank: 7³ = _______

Fill in the blank: The reciprocal of 4³ is _______

True or False: (a × b)ⁿ = aⁿ × bⁿ for all real numbers a, b and integer n.

True or False: (a^m)ⁿ = a^m+n

True or False: 2ⁿ is always even for any positive integer n.

True or False: Any nonzero number raised to the power of zero is 1.