Exercise 1 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong:

$x^0=1$ .

See Positive integer power functions.

Antwoord 3 feedback

Wrong:

$x^{\frac{1}{2}}\cdot x^2 \neq x^1$ .

See Properties power functions.

Antwoord 4 feedback

Wrong:

$(x^{2\frac{1}{2}})^3\neq x^{5\frac{1}{2}}$ .

See Properties power functions.