거듭제곱근과 지수의 확장

Population growth The expression $10\cdot {x}^{n}$ models the growth of a mold population after $n$ generations. There were 10 spores at the start, and each had $x$ offspring. So $10\cdot {x}^{5}$ is the number of offspring at the fifth generation. At the fifth generation there were 10,240 offspring. Simplify the expression $\sqrt[5]{\frac{10,240}{10}}$ to determine the number of offspring of each spore.

Landscaping Joe wants to have a square garden plot in his backyard. He has enough compost to cover an area of 144 square feet. Simplify ${144}^{\frac{1}{2}}$ to find the length of each side of his garden.

Landscaping Elliott wants to make a square patio in his yard. He has enough concrete to pave an area of 242 square feet. Simplify ${242}^{\frac{1}{2}}$ to find the length of each side of his patio.Round to the nearest tenth of a foot.

Gravity While putting up holiday decorations, Bob dropped a decoration from the top of a tree that is 12 feet tall. Simplify $\frac{{12}^{\frac{1}{2}}}{{16}^{\frac{1}{2}}}$ to find how many seconds it took for the decoration to reach the ground. Round to the nearest tenth of a second.

Gravity An airplane dropped a flare from a height of 1024 feet above a lake. Simplify $\frac{{1024}^{\frac{1}{2}}}{{16}^{\frac{1}{2}}}$ to find how many seconds it took for the flare to reach the water.

A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So the length of the guy wire can be found by evaluating $\sqrt{90,000+160,000}.$ What is the length of the guy wire?

A car accelerates at a rate of $6-\frac{\sqrt{4}}{\sqrt{t}}{\,\text{m/s}}^{2}$ where t is the time in seconds after the car moves from rest. Simplify the expression.