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$Rewrite the expression in the form k*x^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). 2sqrtx*4x^(-(5)/(2))=$

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

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Math Problems

Algebra 1

Evaluate variable expressions involving rational numbers

Full solution

Q. Rewrite the expression in the form

k \cdot x^{n}

\newline

Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).

\newline

2 \sqrt{x} \cdot 4 x^{-\frac{5}{2}}=

Understand given expression: First, let's understand the given expression. We have the product of two terms: $2\sqrt{x}$ and $4x^{-(5)/(2)}$ . The term $2\sqrt{x}$ can be written as $2x^{1/2}$ since the square root of $x$ is $x$ to the power of $1/2$ .
Multiply terms with same base: Next, we multiply the two terms together. When multiplying terms with the same base, we add the exponents. So, we will add the exponents $\frac{1}{2}$ and $-\left(\frac{5}{2}\right)$ .
Add exponents: Adding the exponents $\frac{1}{2}$ and $-\frac{5}{2}$ gives us $\frac{1}{2} - \frac{5}{2}$ , which simplifies to $-\frac{4}{2}$ , or $-2$ .
Multiply coefficients: Now, we multiply the coefficients $2$ and $4$ together, which gives us $8$ .
Combine coefficient with exponent: Combining the coefficient with the new exponent, we get the expression in the form $k*x^{n}$ , which is $8x^{-2}$ .