What is the simplified form of the quotient (x^n * y^(2n))/(n^(-1) * y^n) using positive exponents?

What is the simplified form of the quotient (x^n * y^(2n))/(n^(-1) * y^n) using positive exponents?

• A. y^(n) * x^(n)
• B. n * x^n * y^n
• C. x^n / y^{n}
• D. n / (x^n * y^n)

Answer: (B)

To simplify the expression \((x^n * y^{2n})/(n^{-1} * y^n)\), we begin by rewriting \(n^{-1}\) in a more manageable form. The term \(n^{-1}\) can be rewritten as \(1/n\), which allows us to rearrange the expression to: \[ \frac{x^n * y^{2n}}{1/n * y^n} = \frac{x^n * y^{2n}}{y^n} * n \] Next, we apply the laws of exponents. Specifically, when dividing like bases, we subtract the exponents. Here, we have \(y^{2n}/y^n\): \[ y^{2n - n} = y^n \] Now, we substitute this back into our expression: \[ x^n * y^n * n \] This is equivalent to: \[ n * x^n * y^n \] This confirms that the simplified form of the quotient is indeed \(n * x^n * y^n\), making the chosen answer correct. The key steps included recognizing the reciprocal nature of \(n^{-

To simplify the expression ((x^n * y^{2n})/(n^{-1} * y^n)), we begin by rewriting (n^{-1}) in a more manageable form. The term (n^{-1}) can be rewritten as (1/n), which allows us to rearrange the expression to:

[

\frac{x^n * y^{2n}}{1/n * y^n} = \frac{x^n * y^{2n}}{y^n} * n

]

Next, we apply the laws of exponents. Specifically, when dividing like bases, we subtract the exponents. Here, we have (y^{2n}/y^n):

[

y^{2n - n} = y^n

]

Now, we substitute this back into our expression:

[

x^n * y^n * n

]

This is equivalent to:

[

n * x^n * y^n

]

This confirms that the simplified form of the quotient is indeed (n * x^n * y^n), making the chosen answer correct. The key steps included recognizing the reciprocal nature of (n^{-