Simplify the expression. Assume that all variables represent positive real numbers.
-$\frac{5^{3 / 4} x^{-2 / 5} y^{3 / 2}}{5^{-5 / 4} x^{13 / 5} y^{1 / 4}}$

A) $\frac{125 y^{5 / 4}}{x^{3}}$

B) $\frac{25 y^{5 / 8}}{x^{4}}$

C) $\frac{25 y^{5 / 4}}{x^{3}}$

D) $\frac{25 y^{5 / 4}}{x^{2}}$

Question

Simplify the expression. Assume that all variables represent positive real numbers.
-$\frac{5^{3 / 4} x^{-2 / 5} y^{3 / 2}}{5^{-5 / 4} x^{13 / 5} y^{1 / 4}}$

A) $\frac{125 y^{5 / 4}}{x^{3}}$

B) $\frac{25 y^{5 / 8}}{x^{4}}$

C) $\frac{25 y^{5 / 4}}{x^{3}}$

D) $\frac{25 y^{5 / 4}}{x^{2}}$

Quizplus · Accepted Answer

To simplify the given expression, we use the properties of exponents. First, we combine the exponents of like bases by subtracting the exponents in the denominator from those in the numerator:- For the base 5: $5^{3/4} \cdot 5^{-(-5/4)} = 5^{3/4 + 5/4} = 5^{2} = 25$- For the base $x$: $x^{-2/5} \cdot x^{-13/5} = x^{-2/5 - 13/5} = x^{-15/5} = x^{-3}$- For the base $y$: $y^{3/2} \cdot y^{-1/4} = y^{3/2 - 1/4} = y^{6/4 - 1/4} = y^{5/4}$Putting it all together, we get $\frac{25 y^{5/4}}{x^{3}}$.

Simplify the Expression 53/4x−2/5y3/25−5/4x13/5y1/4\frac{5^{3 / 4} x^{-2 / 5} y^{3 / 2}}{5^{-5 / 4} x^{13 / 5} y^{1 / 4}}5−5/4x13/5y1/453/4x−2/5y3/2​

Simplify the Expression $\frac{5^{3 / 4} x^{-2 / 5} y^{3 / 2}}{5^{-5 / 4} x^{13 / 5} y^{1 / 4}}$