3 years ago

Anyone know the answer to this?

Mathematics

1 answer:

jolli1 [7]3 years ago

8 0

Answer:

i think it is A but if i am wrong i am sorry

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3 years ago

Which of the following is the quotient of b and a?

vlabodo [156]

$\bf 19^{\frac{7}{4}}\cdot \sqrt[a]{19^b}=19^{\frac{5}{2}}\sqrt{19}\\\\
-----------------------------\\\\
a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-----------------------------\\\\
thus\qquad 19^{\frac{7}{4}}\cdot 19^{\frac{b}{a}}=19^{\frac{5}{2}}\cdot 19^{\frac{1}{2}}\implies 19^{\frac{7}{4}+\frac{b}{a}}=19^{\frac{5}{2}+\frac{1}{2}}
\\\\\\
$

$\bf 19^{\frac{7}{4}+\frac{b}{a}}=19^{\frac{6}{2}}\implies 19^{\frac{7}{4}+\frac{b}{a}}=19^3\impliedby 
\begin{array}{llll}
\textit{same base, thus}\\
\textit{exponents must be the same}
\end{array}
\\\\\\
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