- Simplify: \( \displaystyle \left( x^{-1} - y^{-1} \right)^{-1} \)
Solution
\( \displaystyle \frac{xy}{y-x} \)
- Simplify: \( \displaystyle \frac{x^{-1} + y^{-1}}{x^{-2}-y^{-2}} \)
Solution
\( \displaystyle \frac{xy}{y-x} \)
- Simplify: \( \displaystyle \sqrt[3]{x^2} \cdot \sqrt[5]{x^3} \cdot \sqrt[6]{x} \)
Solution
\( \displaystyle x\sqrt[30]{x^{13}} \)
- Simplify: \( \displaystyle \sqrt{a \cdot \sqrt[3]{a}} \)
Solution
\( \displaystyle \sqrt[3]{a^2} \)
- Simplify: \( \displaystyle \left( \frac{27^{\frac{4}{3}} - 27^0}{ \left( 3^2 + 4^2 \right)^{\frac{1}{2}}} \right)^ \frac{3}{4} \)
Solution
\( \displaystyle 8 \)
- Simplify: \( \displaystyle \left( \frac{a^{-2}b^{\frac{2}{3}}}{b^{-\frac{1}{2}}} \right)^{-4} \)
Solution
\( \displaystyle \frac{a^8}{b^{\frac{14}{3}}} \)
- Simplify: \( \displaystyle \frac{3^{-1}}{3^{-2}+3^{-3}} \)
Solution
\( \displaystyle \frac{9}{4} \)
- Solve: \( \displaystyle 4^{x+1} = \left( \frac{1}{2} \right)^{-3x} \)
Solution
\( \displaystyle 2 \)
- Solve: \( \displaystyle 2^{4x}\cdot 4^{x - 3} = 64^{x - 1} \)
Solution
\( \displaystyle x \in \mathbb{R} \)
- Solve: \( \displaystyle 3 \left( x - 4 \right)^{\frac{1}{2}} = 15 \)
Solution
\( \displaystyle 29 \)
- Solve: \( \displaystyle x^{\frac{2}{3}} - 3x^{\frac{1}{3}} = -2 \)
Solution
\( \displaystyle x = \{ 1, 8 \} \)