Exponentiation - practice problems
If n is a positive integer and x is any real number, then x^n corresponds to repeated multiplication x^n=x×x×⋯×x (n times). We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” Here, x is the base, and n is the exponent or the power.Exponents, also known as powers, are values that show how many times to multiply a base number by itself. For example, 23 is telling you to multiply two by itself three times.
Exponents and powers.
Number of problems found: 280
- Doubling every day
If you start with 1 euro on day 1 and double your money daily, how many days before you get at least 1 million? - Daily compounded
Zachary invested $130 in an account paying an interest rate of 3.6% compounded daily, Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 11 years? - Simplify complex expr
Perform the indicated operations and write the results in the form of a + bi: (2 + 3i)³ (ii) (1 + i)⁴ - A student 8
A student was asked to write 25 * 9² . By mistake he write 2592. Find the difference.
- Population growth 2
The present population of the town is 200,000. Its population increases by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years. - The cost 15
The cost of a machine depreciates every year by 10% of its cost at the beginning of the year. If the present cost of the machine is USD 10000, find its cost after 2 years. - Divisors 7
If 540=2²×3³×5, what is the number of all factors of 540? - Interest over time
If certain sum at compound interest becomes double in 5 years, then, in how many years, it will be 16 times at the same rate of interest? - Per annum At a certain time, a sum becomes 4 times at the rate of 5% per annum. At what rate of simple interest the same sum becomes 8 times in the same duration
- A pattern
If I have a pattern that starts with 1, 4, 9, 16, 25... and so on, which of the following numbers would not appear? - The enrolment 2 The enrolment at a school has increased from 1400 learners to 1600 learners over 5 years. What is the percentage increase in enrolment?
- Powers of three
Simplify to a single power of 3: 35/3 Words: start fraction, 3, to the power 5, divided by, 3, end fraction. - HCF of polynoms Find the HCF of the given expression: 2a²b²c4, 2a4b³c³ and 4a²b³
- Compound interest
Joel borrowed $3208.5 on November 2, 2021, at 3.6% p.a. How many days would it take for him to repay the loan if he made a payment of $ 3,720.34? Round up to the nearest day.
- Perfect square or cube
Would you classify 324 as a perfect square, perfect cube, both, or neither? ... - The sum 41 The sum of 640.00 was deposited in the first bank for five years, and the interest given was 160.00. Find the rate.
- A cube 3
A cube of edge 100 cm has the same volume as a cube of edge 1 m. how many cubic centimeters make 1 cubic meter? - The balance 2 If your balance at the end of 4 years is 50000, at a 5% interest rate, What was your original investment?
- Years 3 How long will it take for a given sum of money to triple itself at 20% annual compound interest?
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