 Recent questions in Exponents and radicals
ANSWERED ### Find the distance between the pair of points (3.5, 8.2) and (-0.5, 6.2). If necessary, express answers in simplified radical form and then round to two decimals places.

ANSWERED ### Find, to the nearest tenth of a second, the period of a pendulum of length 3.5 feet.

ANSWERED ### Find the rectangular coordinates of the pair of points $$\displaystyle{\left({6},\pi\right)}$$ and $$\displaystyle{\left({5},{7}\frac{\pi}{{4}}\right)}$$. Then find the distance, in simplified radical form, between the points.

ANSWERED ### Simplify and express the final result using positive exponents. $$\displaystyle{\left({\frac{{{8}{y}^{{2}}}}{{{2}{y}^{{-{1}}}}}}\right)}^{{-{1}}}$$

ANSWERED ### Expand the expression and write your answer without the exponents. $$\displaystyle{{\log}_{{4}}{\frac{{{x}^{{2}}{y}^{{4}}}}{{{8}}}}}$$

ANSWERED ### Solve for the following exponential equations. Use the natural logarithm in your answer(where applicable) for full credit. Use rules for exponents, factor and simplify. $$\displaystyle{10}^{{{6}-{3}{x}}}={18}$$

ANSWERED ### Simplify and express the final result using positive exponents. $$\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}$$

ANSWERED ### Model the following data using an exponential function of the form $$\displaystyle{f{{\left({x}\right)}}}={A}{b}^{{x}}$$ . Set up a system of equations, and solve it to get A and b. f(x) is exponential and goes through the points (1, 2) and (4, 6).

ANSWERED ### Solve the exponential equation $$\displaystyle{6}^{{\frac{{{x}-{3}}}{{4}}}}=\sqrt{{{6}}}$$ by expressing each side as a power of the same base and then equating exponents.

ANSWERED ### Solve the exponential equation $$3^x=81$$ by expressing each side as a power of the same base and then equating exponents.

ANSWERED ### Simplify and express the final result using positive exponents. $$\displaystyle{\left({\frac{{{4}{a}^{{-{2}}}}}{{{3}{b}^{{-{2}}}}}}\right)}^{{-{2}}}$$

ANSWERED ### A function value and a quadrant are given. Find the other five function values. Give exact answers, uing radicals as needed. Rationalize all denominators. $$\displaystyle{\cot{\theta}}=-{4}$$, Quandrant 4

ANSWERED ### Solve for the following exponential equations. Use the natural logarithm in your answer(where applicable) for full credit. Use rules for exponents, factor and simplify. $$\displaystyle{4}^{{{1}-{x}}}={3}^{{{2}{x}+{5}}}$$

ANSWERED ### Adding and subtracting radicals $$\displaystyle{2}{x}\sqrt{{{3}{x}^{{2}}{y}}}\cdot{3}\sqrt{{{15}{x}{y}^{{3}}}}$$

ANSWERED ### Simplify, $$\displaystyle{4}\sqrt{{{18}}}+{5}\sqrt{{{27}}}-{8}\sqrt{{{32}}}$$

ANSWERED ### For the exponential fuction $$\displaystyle{f{{\left({x}\right)}}}={10}^{{x}}$$, find $$\displaystyle f{{\left(\frac{3}{{2}}\right)}}$$ $$\displaystyle f{{\left(\frac{3}{{2}}\right)}}=?$$ Type an exact answer, using radicals as needed.

ANSWERED ### Use the properties of logarithms to rewrite each expression as the logarithm of a single expression. Be sure to use positive exponents and avoid radicals.

ANSWERED ### Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. $$\displaystyle{3}^{{{1}-{x}}}={\frac{{{1}}}{{{27}}}}$$

ANSWERED ### Find the solution: $$\displaystyle{6}=\sqrt{{{x}^{{2}}-{2}{x}+{12}}}$$
ANSWERED 