Question

rewrite the expression in the form $k \cdot x^n$. write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $2\sqrt{x} \cdot 4x^{\frac{-5}{2}} = $

Explanation:

Step1: Simplify the coefficients

Multiply the coefficients 2 and 4.
\(2\times4 = 8\)

Step2: Simplify the variable terms

Recall that \(\sqrt{x}=x^{\frac{1}{2}}\). So we have \(x^{\frac{1}{2}}\cdot x^{-\frac{5}{2}}\). Using the rule of exponents \(a^m\cdot a^n=a^{m + n}\), we get \(\frac{1}{2}+(-\frac{5}{2})=\frac{1 - 5}{2}=\frac{-4}{2}=-2\). So the variable part is \(x^{-2}\).

Step3: Combine the coefficient and variable

Multiply the coefficient from Step1 and the variable part from Step2. So we have \(8\cdot x^{-2}\).

Answer:

\(8x^{-2}\)