Questions: For nonzero x and y, (3x^12y^7)/(2x^6y) is equivalent to? (A) (3x^2y^7)/2 (B) (3x^18y^8)/2 (C) (3x^6y^6)/2 (D) 3x^6y^6 (E) x^6y^6

Transcript text: For nonzero $x$ and $y, \frac{3 x^{12} y^{7}}{2 x^{6} y}$ is equivalent to? (A) $\frac{3 x^{2} y^{7}}{2}$ (B) $\frac{3 x^{18} y^{8}}{2}$ (C) $\frac{3 x^{6} y^{6}}{2}$ (D) $3 x^{6} y^{6}$ (E) $x^{6} y^{6}$

Solution

Solution Steps

To simplify the expression $\frac{3 x^{12} y^{7}}{2 x^{6} y}$, we need to apply the properties of exponents. Specifically, we will divide the coefficients and subtract the exponents of like bases in the numerator and the denominator.

Step 1: Simplifying the Expression

We start with the expression

\[ \frac{3 x^{12} y^{7}}{2 x^{6} y} \]

Step 2: Dividing the Coefficients

First, we divide the coefficients:

\[ \frac{3}{2} \]

Step 3: Simplifying the Exponents of $x$

Next, we simplify the exponents of $x$:

\[ x^{12} \div x^{6} = x^{12 - 6} = x^{6} \]

Step 4: Simplifying the Exponents of $y$

Now, we simplify the exponents of $y$:

\[ y^{7} \div y^{1} = y^{7 - 1} = y^{6} \]