select the correct answer. which expression is equivalent to the given expression? assume the denominator…

select the correct answer. which expression is equivalent to the given expression? assume the denominator does not equal zero. $\frac{a^{3}b^{5}}{a^{4}b}$\na. $\frac{b^{4}}{a}$\nb. $\frac{a}{b^{4}}$\nc. $\frac{1}{ab^{4}}$\nd. $ab^{4}$

select the correct answer. which expression is equivalent to the given expression? assume the denominator does not equal zero. $\frac{a^{3}b^{5}}{a^{4}b}$\na. $\frac{b^{4}}{a}$\nb. $\frac{a}{b^{4}}$\nc. $\frac{1}{ab^{4}}$\nd. $ab^{4}$

Answer

Explanation:

Step1: Aplicar la regla de exponentes $\frac{x^m}{x^n}=x^{m - n}$ para $a$ y $b$

$\frac{a^{3}b^{5}}{a^{4}b}=\frac{a^{3}}{a^{4}}\cdot\frac{b^{5}}{b}$

Step2: Calcular $\frac{a^{3}}{a^{4}}$

$\frac{a^{3}}{a^{4}}=a^{3 - 4}=a^{- 1}=\frac{1}{a}$

Step3: Calcular $\frac{b^{5}}{b}$

$\frac{b^{5}}{b}=b^{5 - 1}=b^{4}$

Step4: Multiplicar los resultados

$\frac{1}{a}\cdot b^{4}=\frac{b^{4}}{a}$

Answer:

A. $\frac{b^{4}}{a}$