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  3. Chapter 1: Functions of one variable
  4. Exponential and logarithmic functions
  5. Properties exponential functions
  6. Exercise

Exercise

Determine $p$ such that $\dfrac{5^2\cdot 5^8}{(5^3)^4}=5^p$.
$p=-2$
$p=4$
$p=3$
$p=\frac{10}{12}$
Determine $p$ such that $\dfrac{5^2\cdot 5^8}{(5^3)^4}=5^p$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$p=4$
Antwoord 2 correct
Fout
Antwoord 3 optie
$p=3$
Antwoord 3 correct
Fout
Antwoord 4 optie
$p=\frac{10}{12}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$p=-2$
Antwoord 1 feedback
Correct: $$\begin{align*}
\frac{5^2\cdot 5^8}{(5^3)^4} & = \frac{5^{10}}{(5^3)^4} \\
& = \frac{5^{10}}{5^{12}}\\
& = 5^{-2}.
\end{align*}$$

Go on.
Antwoord 2 feedback
Wrong: $5^2 \cdot 5^8 \neq 5^{16}$.

See Properties exponential functions.
Antwoord 3 feedback
Wrong: $(5^3)^4\neq 5^7$.

See Properties exponential functions.
Antwoord 4 feedback
Wrong: $\dfrac{5^{10}}{5^{12}}\neq 5^{\frac{10}{12}}$.

See Properties exponential functions.