Exponentiation - practice problems - page 5 of 14
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: 270
- Cube construction
A 2×2×2 cube will be constructed using four white and four black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. ) - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - Before yesterday
The merchant adds a sale sign in his shop window to the shown pair of shoes in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the - Compound interest 3
After eight years, what is the total amount of a compound interest investment of $25,000 at 3% interest, compounded quarterly? (interest is now a dream - in the year 2019) - Divide 8
Divide 6840 by x, y, and z in such a way that x has twice as much as y, who has half as much as z - The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets and their products was the power of the prime number. Find all possible ticket prices. - Six speeds
A drilling machine is to have six speeds ranging from 50 to 750 revolutions per minute. If the speed forms a geometric progression, determine their values. - Three members GP
The sum of three numbers in GP (geometric progression) is 21, and the sum of their squares is 189. Find the numbers. - Eq2 2
Solve the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23 - Investment 2
Jack invested $5000 in a 5-month term deposit at 4.7% pa. At the end of the five months, Jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% pa. What is the maturity value at the end of the second term deposit? - Exponential 8360
Solve the exponential equation: 8 raised to x = 40 - Curiosity factor
A blogger starts a new website. Initially, the number of traffic was 293 due to their curiosity factor. The business owner estimated that the traffic would increase by 2,6% per week. What will be the number of it in week 5? - The machine
The annual depreciation of the machine is 10%. After eight years, the machine is worth 697 euros. What was the price of this machine at the time of purchase? - Profit growth
A company's profit increased by 25% during 1992, increased by 40% during 1993, decreased by 20% in 1994, and increased by 10% during 1995. Find the average growth in the profit level over the four years periods. - Expression: 7974
Number 1 is the value of the expression: a 5-3 b. 22 - 32 c. (2 - 3)² d. 2 - 32 e. 32 - 22 - Determine 7488
The lengths of the edges of the two cubes are in the ratio 2:3. Determine how many times the surface of the larger cube is larger than the surface of the smaller cube. - Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Kilometers 7415
The Earth's distance from the moon is 3,844.10 to the eighth meter. How many kilometers is it? - Precious metals
From 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, and silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41. - Cube surface and volume
Find the surface of the cube with a volume of 27 dm³.
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