Simplify expressions involving exponents Precalculus

Simplify the following expressions in which a, x and y are real numbers greater than 0.

\dfrac{a^3.a^{-2}.a^{1/4}}{a^2.a^{-1}}

a^{-3/4}

a^{1/4}

a^{-1/4}

\dfrac{2\times2^{-2}\times2^{4}}{2^{3}\times2^{1/2}}

\dfrac{\sqrt{2}}{2}

{\sqrt{2}}

2\sqrt{2}

\dfrac{a^3.a^{-1/2}}{a^2.a^{1/2}.a}

a^{3/4}

a^{1/4}

\dfrac{1}{a}

\dfrac{2^{3/2}.x^3.y^{-2}}{2^{5/2}.x^{1/3}.y^{1/2}}

\dfrac{1}{2}. x^{4/3} .y^{-5/2}

2. x^{4/3} .y^{5/2}

2. x^{8/3} .y^{-5/2}

\dfrac{1}{2} . x^{8/3} .y^{-5/2}

\dfrac{\left(a^3.a^{-1/4}\right)^4}{\left(a^{1/3}.a^{-1/2}\right)^3}\\\\\\

a^{19/2}

a^{11}

a^{23/2}

a^{-19/2}

\dfrac{4\times 5^{-1/2}\times 5^{3}}{5^{4}\times 4^{1/2}}

5^{-3/2}

2 \times 5^{-3/2}

\dfrac{1}{2} \times 5^{-3/2}

\dfrac{1}{2}\times 5^{3/2}

\dfrac{\left(a^3.b^{-1/6}\right)^3}{\left(a^{-2}.b^{-1/2}\right)^2}\\\\\\

a^{-3/4}

a^{1/4}

a^{-1/4}