Exercise 3 | Wiskunde op Tilburg University

Solve

$16\cdot (2x^2)^4 = (8x^3)^5 \cdot (\frac{1}{4x^4})^2$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$x=16^{\frac{1}{15}}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$x=8^{\frac{8}{15}}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$x=\frac{1}{16}$ .

Antwoord 4 correct

Fout

Antwoord 1 optie

$x=8$

Antwoord 1 feedback

Correct:

$\begin{align*} 16\cdot (2x^2)^4 = (8x^3)^5 \cdot (\frac{1}{4x^4})^2 &\Leftrightarrow 2^4(2x^2)^4=(2^3x^3)^5 \cdot (2^{-2}x^{-4})^2\\ & \Leftrightarrow 2^4\cdot 2^4 \cdot x^8=2^{15}\cdot x^{15} \cdot 2^{-4}\cdot x^{-8}\\ & \Leftrightarrow 2^8 \cdot x^8=2^{11}\cdot x^7\\ & \Leftrightarrow x=2^3\\ & \Leftrightarrow x=8. \end{align*}$

Go on.

Antwoord 2 feedback

Wrong:

$16 \cdot (2x^2)^4 \neq 32x^8$ .

See Properties power functions.

Antwoord 3 feedback

Wrong:

$\dfrac{x^{15}}{x^8} \neq x^{\frac{15}{8}}$ .

See Properties power functions.

Antwoord 4 feedback

Wrong:

$16 \cdot (2x^2)^4 \neq 32x^8$ .

See Properties power functions.