Determine $p$ and $q$ such that $\dfrac{(\sqrt{x}\cdot y^5 \cdot x^2)^3}{\sqrt[3]{y^6}\cdot \sqrt[2]{x^{15}}}=x^p\cdot y^q$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$p=1$, $q=13$
Antwoord 2 correct
Fout
Antwoord 3 optie
$p=-4\frac{1}{2}$, $q=13$
Antwoord 3 correct
Fout
Antwoord 4 optie
$p=-2$, $q=13$
Antwoord 4 correct
Fout
Antwoord 1 optie
$p=0$, $q=13$
Antwoord 1 feedback
Correct: $$\begin{align*}
\frac{(\sqrt{x} \cdot y^5 \cdot x^2) ^3}{\sqrt[3]{y^6}\cdot \sqrt[2]{x^{15}}} & = \frac{( x^{\frac{1}{2}} \cdot y^5 \cdot x^2 )^3}{y^{\frac{6}{3}} \cdot x^ {\frac{15}{2}}}\\
& = \frac{ (x^{2\frac{1}{2}}\cdot y^5)^3}{y^2\cdot x^{7\frac{1}{2}}}\\
& = \frac{(x^{2\frac{1}{2}})^3\cdot (y^5)^3}{y^2\cdot x^{7\frac{1}{2}}}\\
& = \frac{ x^{7\frac{1}{2}}\cdot y^{15} }{y^2\cdot x^{7\frac{1}{2}} }\\
& = x^0\cdot y^{13}\\
& = y^{13}.
\end{align*}$$
Hence, $p=0$ and $q=13$.
Go on.
\frac{(\sqrt{x} \cdot y^5 \cdot x^2) ^3}{\sqrt[3]{y^6}\cdot \sqrt[2]{x^{15}}} & = \frac{( x^{\frac{1}{2}} \cdot y^5 \cdot x^2 )^3}{y^{\frac{6}{3}} \cdot x^ {\frac{15}{2}}}\\
& = \frac{ (x^{2\frac{1}{2}}\cdot y^5)^3}{y^2\cdot x^{7\frac{1}{2}}}\\
& = \frac{(x^{2\frac{1}{2}})^3\cdot (y^5)^3}{y^2\cdot x^{7\frac{1}{2}}}\\
& = \frac{ x^{7\frac{1}{2}}\cdot y^{15} }{y^2\cdot x^{7\frac{1}{2}} }\\
& = x^0\cdot y^{13}\\
& = y^{13}.
\end{align*}$$
Hence, $p=0$ and $q=13$.
Go on.
Antwoord 2 feedback
Antwoord 3 feedback
Antwoord 4 feedback