AP®︎ Precalculus: Topic 2.4 Practice Test

Essential Knowledge: 2.4.A.1

The product property for exponents states that $b^m b^n = b^{(m+n)}$. Graphically, this property implies that every horizontal translation of an exponential function, $f(x) = b^{(x+k)}$, is equivalent to a vertical dilation, $f(x) = b^{(x+k)} = b^x b^k = ab^x$, where $a = b^k$.

Essential Knowledge: 2.4.A.2

The power property for exponents states that $(b^m)^n = b^{(mn)}$. Graphically, this property implies that every horizontal dilation of an exponential function, $f(x) = b^{(cx)}$, is equivalent to a change of the base of an exponential function, $f(x) = (b^c)^x$, where $b^c$ is a constant and $c \ne 0$.

Essential Knowledge: 2.4.A.3

The negative exponent property states that $b^{-n} = \frac{1}{b^n}$.

Essential Knowledge: 2.4.A.4

The value of an exponential expression involving an exponential unit fraction, such as $b^{(1/k)}$ where $k$ is a natural number, is the $k$th root of $b$, when it exists.