Questions: QUESTION 13 Simplify: [ frac(x^3 y^2)(x^5 y^7)x^2 y^5 ]

$QUESTION 13 Simplify: [ frac(x^3 y^2)(x^5 y^7)x^2 y^5 ]$

Transcript text: QUESTION 13 Simplify: \[ \frac{\left(x^{3} y^{2}\right)\left(x^{5} y^{7}\right)}{x^{2} y^{5}} \]

Solution

Solution Steps

Step 1: Write the Original Expression

We start with the expression: \[ \frac{\left(x^{3} y^{2}\right)\left(x^{5} y^{7}\right)}{x^{2} y^{5}} \]

Step 2: Apply the Laws of Exponents

Using the laws of exponents, we can simplify the expression. When multiplying terms with the same base, we add the exponents. When dividing, we subtract the exponents. Thus, we can rewrite the expression as: \[ \frac{x^{3+5} y^{2+7}}{x^{2} y^{5}} = \frac{x^{8} y^{9}}{x^{2} y^{5}} \]

Step 3: Simplify the Expression

Now, we apply the division of exponents: \[ x^{8-2} y^{9-5} = x^{6} y^{4} \]