# Get help with rational exponents and radicals Recent questions in Rational exponents and radicals
ANSWERED ### The simplified form of the expression$$\displaystyle{\sqrt[{{3}}]{{a}}}{\sqrt[{{6}}]{{a}}}\ \text{in radicalnotation is}\ \sqrt{a}.$$

ANSWERED ### Use a right triangle to write the following expression as an algebraic expression. Assume that x is positive and in the domain of the given inverse trigonometric function. Given: $$\displaystyle \tan{{\left({{\cos}^{ -{{1}}}{5}}{x}\right)}}=?$$

ANSWERED ### Combining radicals simplify the expression. Assume that all letters denote positive numbers. $$\displaystyle\sqrt{{{16}{x}}}+\sqrt{{{x}^{5}}}$$

ANSWERED ### The given expression using rational exponents. Then simplify and convert back to radical notation. Assume that all variables represent positive real numbers. Given: The expression is $$\displaystyle\sqrt{{{81}{a}^{12}{b}^{20}}}$$

ANSWERED ### Find the exact value of each of the remaining trigonometric function of $$\theta.$$ $$\displaystyle \cos{\theta}=\frac{24}{{25}},{270}^{\circ}<\theta<{360}^{\circ}$$ $$\displaystyle \sin{\theta}=?$$ $$\displaystyle \tan{\theta}=?$$ $$\displaystyle \sec{\theta}=?$$ $$\displaystyle \csc{\theta}=?$$ $$\displaystyle \cot{\theta}=?$$

ANSWERED ### For the following exercises, use the compound interest formula, $$\displaystyle{A}{\left({t}\right)}={P}{\left({1}+\frac{r}{{n}}\right)}^{{{n}{t}}}$$. Use properties of rational exponents to solve the compound interest formula for the interest rate, r.

ANSWERED ### Use rational exponents to write a single radical expression. $$\displaystyle{\sqrt[{{7}}]{{11}}}\times{\sqrt[{{6}}]{{13}}}$$

ANSWERED ### Simplify each expression (a) $$\displaystyle{\sqrt[{{4}}]{{{3}^{2}}}}$$ (b) $$\displaystyle{\sqrt[{{6}}]{{{\left({x}+{1}\right)}^{4}}}}$$

ANSWERED ### Rationalize the denominator. $$\displaystyle\frac{\sqrt{{40}}}{\sqrt{{56}}}$$

ANSWERED ### The simplified form of the expression $$\displaystyle{\sqrt[{{4}}]{{{c}{d}^{2}}}}\times{\sqrt[{{3}}]{{{c}^{2}{d}}}}.$$

ANSWERED ### a) Find the rational zeros and then the other zeros of the polynomial function $$\displaystyle{\left({x}\right)}={x}^{3}-{4}{x}^{2}+{2}{x}+{4}, \text{that is, solve}\ \displaystyle f{{\left({x}\right)}}={0}.$$ b) Factor $$f(x)$$ into linear factors.

ANSWERED ### To calculate: The simplified form of the expression $$\displaystyle\frac{\sqrt{{12}}}{\sqrt{{{x}+{1}}}}.$$

ANSWERED ### To calculate: The expression $$\displaystyle\frac{{2.7}^{{-{11}\text{/}{12}}}}{{2.7}^{{-{1}\text{/}{6}}}}$$ with positive exponent.

ANSWERED ### To rationalize: Each numerator. Assume that variables represent positive real numbers. Given: An expression : $$\displaystyle\frac{{\sqrt[{{3}}]{{9}}}}{{7}}.$$

ANSWERED ### Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. $$\displaystyle\sqrt{{{x}^{3}}}$$

ANSWERED ### To multiply: The given expression. Then simplify if possible. Assume that all variables represent positive real numbers. Given: An expression: $$\displaystyle\sqrt{{3}}{\left(\sqrt{{27}}-\sqrt{{3}}\right)}$$

ANSWERED ### To calculate: The simplified value of the radical expression $$\displaystyle\sqrt{{{18}{a}}}\div\sqrt{{{2}{a}^{4}}}.$$

ANSWERED ### The values of x that satisfy the equation with rational exponents $$\displaystyle{x}^{{\frac{3}{{2}}}}={8}$$ and check all the proposed solutions.

ANSWERED ### To simplify: The given redical: An expression: $$\displaystyle{\sqrt[{{4}}]{{{\left({x}^{2}-{4}\right)}^{4}}}}.$$ Use absolute value bars when necessary.
ANSWERED 