Final answer:
To simplify the expression (14x⁵y³*3x⁴y⁹)/(6x³y⁴), multiply the coefficients, apply the exponent rules to combine like bases, and then divide the numerator by the denominator terms to get 7x⁶y⁸.
Step-by-step explanation:
The question asks to simplify the mathematical expression (14x⁵y³*3x⁴y⁹)/(6x³y⁴). To simplify this expression, we apply the laws of exponents and division. First, we multiply the coefficients (numbers) and then apply the exponent rules separately for the x's and y's.
Step-by-step simplification:
- Multiply the coefficients: 14 * 3 = 42.
- Combine the x terms using the exponent rule (a⁻m * a⁻n = a⁻(m+n)): x⁵ * x⁴ = x⁹.
- Combine the y terms using the similar exponent rule: y³ * y⁹ = y¹².
- Divide by the denominator: (42x⁹y¹²)/(6x³y⁴).
- Simplify coefficients by division: 42 / 6 = 7.
- Subtract the exponents for x (using a⁻m / a⁻n = a⁻(m-n)): x⁹ / x³ = x⁶.
- Subtract the exponents for y: y¹² / y⁴ = y⁸.
Putting it all together, the simplified expression is 7x⁶y⁸.
The complet question is:content loaded
owing is the simplified form of the expression given be (14x⁵y³*3x⁴y⁹)/(6x(3)y⁴)