Final answer:
To simplify 3y6 over 9y3, divide the coefficients and subtract the exponents, resulting in a simplified expression of 1/3y3.
Step-by-step explanation:
The student's question is about simplifying the expression 3y6 over 9y3. To simplify this expression, we need to divide the numerator by the denominator. Since 3y6 and 9y3 both have the variable y with exponents, we apply the laws of exponents during division.
When dividing exponents with the same base, we subtract the exponents. Therefore, y6 divided by y3 gives us y6-3 or y3. Additionally, dividing the numerical coefficients gives us 3 divided by 9, which simplifies to 1/3. Combining these results, we get 1/3y3 as the simplified expression.
Here is the step-by-step process:
- Divide the coefficients: 3 ÷ 9 = 1/3.
- Subtract the exponents: y6 ÷ y3 = y6-3 = y3.
- Combine the results: 1/3 * y3 = 1/3y3.
To simplify the expression 3y^6 over 9y^3, we can divide the numerators and denominators separately. Dividing 3y^6 by 9 gives us (3/9)y^6. Simplifying 3/9 further, we get 1/3. Dividing y^6 by y^3, we subtract the exponents and get y^(6-3) = y^3. Putting it all together, the simplified expression is 1/3 y^3.