Which is equivalent to [tex]$80^{\frac{1}{4} x}$[/tex]?
A. [tex]$\left(\frac{80}{4}\right)^x$[/tex]
B. [tex]$\sqrt[4]{80}^x$[/tex]
C. [tex]$\sqrt[x]{80^4}$[/tex]
D. [tex]$\left(\frac{80}{x}\right)^4$[/tex]
Answer (2)
The equivalent expression is 4 80 x .
Examples
Understanding exponential expressions is crucial in various fields, such as finance and physics. For instance, when calculating compound interest, the formula often involves terms with fractional exponents. Similarly, in physics, exponential decay models, like those used to describe radioactive decay, utilize similar mathematical concepts. By mastering these concepts, you can analyze and predict outcomes in real-world scenarios involving growth or decay processes.
The expression 8 0 4 1 x can be rewritten as ( 4 80 ) x . Among the options provided, the equivalent expression is choice B : 4 80 x . Thus, the final answer is 4 80 x .
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