Exponentiation + square (second power, quadratic) - practice problems

Number of problems found: 54

Finite geometric sequence
Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 18, an = 13122, sn = 19674, n =?, q =?
Seventh term
The first term of a geometric sequence is 9 and the third term is 1296. Find the seventh term.
Sq and cube
Find the product of the square of (1/2) and the cube of (2/3)
Future value investment
Poseidon deposited 2,747 golden drachmas in a Mount Olympus college savings account to ensure Percy can go to college. It pays 0.04 (percent in decimal form) annual interest. After 11 years, he withdraws the money. How much more money would he have if the
Annual increase
The number of cars produced increased from 45,000 to 47,000 in 3 years. Calculate the average annual increase in cars in%.
Percentage increase
What is the annual percentage increase in the city when the population has tripled in 20 years?
Simplest form
Find the simplest form of the following expression: 3 to the 2nd power - 1/4 to the 2nd power.
Volume of wood
Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p?
A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
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, as well as their product, was the power of the prime number. Find all possible ticket prices.
Six speeds
A drilling machine is to have 6 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.
Profit growth
The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?
Substitution method
Solve goniometric equation: sin⁴ θ - 1/cos² θ=cos² θ - 2
Precious metals
In 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 -41.3
Cube surface and volume
Find the surface of the cube with a volume of 27 dm³.
Find the 2
Find the term independent of x in the expansion of (4x³+1/2x)⁸
Cube
One cube has an edge increased five times. How many times will larger it's surface area and volume?
Exponential equation
Find x, if 625 ^ x = 5 The equation is exponential because the unknown is in the exponential power of 625
Unknown number 17
Milada said, I am thinking of a number such that I evaluate expression x¹/3, the value of the expression would be 5. Which number Milada thinking?

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Exponentiation - practice problems. Square (second power, quadratic) - practice problems.