Question

answer the question below. type your response in the space provided. use the scientific calculator given in this course to simplify $8^{sqrt{3}}$. 13.856. try again incorrect. to simplify press 8, then the exponent button, then 3, and the equal sign (=) on the calculator. try again.

Explanation:

Step1: Identify the operation

We need to calculate \(8^{\sqrt{3}}\). First, recall that \(\sqrt{3}\approx1.732\).

Step2: Use a calculator for exponentiation

Using a scientific calculator, we input \(8\), then the exponent button, then \(\sqrt{3}\) (or its approximate value \(1.732\)), and then press equals.
Calculating \(8^{1.732}\):
We know that \(8 = 2^3\), so \(8^{\sqrt{3}}=(2^3)^{\sqrt{3}} = 2^{3\sqrt{3}}\approx2^{5.196}\).
Using a calculator, \(2^{5.196}\approx22.627\) (or directly calculating \(8^{\sqrt{3}}\) gives approximately \(22.627\)).

Answer:

\(22.627\) (approximate value, more precise calculation can be done with a scientific calculator)