Question

Divide x to the 3 fourths power divided by x to the 1 sixth power

x to the 7 twelfths power

x to the 11 twelfths power

x to the 1 sixth power

x

Answer 1

\(\bf \large{\cfrac{1}{a^{\color{red} n}}=a^{-{\color{red} n}}
\\ \quad \\ \quad \\
\cfrac{x^{\frac{3}{4}}}{x^{\frac{1}{6}}}\implies \cfrac{x^{\frac{3}{4}}}{1}\cdot \cfrac{1}{x^{{\color{red}{ \frac{1}{6}}}}}\implies x^{\frac{3}{4}}\cdot x^{-{\color{red}{ \frac{1}{6}}}}}\)

Answer 2

http://www.math-play.com/image-exponents-rules.jpg <-- notice the 1st rule there