Exponential Expressions and Equations

Exponential expressions are essentially numbers that have been elevated to a certain power, for instance, 2^3. Exponential equations, on the other hand, are equations that include these expressions, such as 2^x = 8. These equations are particularly useful in illustrating patterns of growth or decay and can be resolved by employing logarithms or factoring methods. They find significant applicability in sectors such as science, finance, and engineering.

Exponential Expressions

Select the expression which is not equivalent to: \[ a^{2} b^{-3} c^{1.5} \] a) $\frac{a^{1.5} c^{2}}{\sqrt[4]{a^{-2} b^{12} c^{2}}}$ b) $\frac{\left(a^{-2} b^{-2} c^{3}\right)\left(a^{-2} b^{2} \sqrt{c^{-3}}\right)}{a^{-6} b^{2}}$ c) $\frac{a^{3} b^{-1} c^{3}}{\sqrt{a^{2} b^{4} c^{3}}}$

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Exponential Equations

An SUV is purchased new for $\$ 31,500$. (b) Suppose that the vehicle is depreciated so that it holds only $90 \%$ of its value from the previous year. Write an exponential function of the form $y=V_{0} b^{t}$, where $V_{0}$ is the initial value and $t$ is the number of years after purchase. The model for the value of the vehicle $t$ years after purchase is $y=$

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Converting to Radical Form

Convert the exponential expression $2^{3/4}$ to its radical form.

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Find the Nth Root of the Given Value

Find the cube root of 27.

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Exponential Expressions and Equations