Question

Simplify the expression ( -6x²y³)⁴ / (8x⁹) times 3xy⁵.

a) -27y² / x²
b) -81y² / x²
c) 27y² / x²
d) 81y² / x²

Answer 1

To simplify the given expression, you apply the exponent, divide, and multiply as per the order of operations, which results in the simplified form -81y² / x², corresponding to option (b).

Step-by-step explanation:

To simplify the expression ( -6x²y³)⁴ / (8x⁹) times 3xy⁵, we follow these steps:

1. Apply the exponent of 4 to each term in the first expression: (-6´)(x²⁴)(y³⁴).
   This simplifies to 1296x⁸y¹².
2. Divide 1296x⁸y¹² by 8x⁹. This gives us 162x⁻¹y¹² when we simplify.
3. Multiply the result by 3xy⁵: 162x⁻¹y¹² * 3xy⁵. This results in 486y·/x.
4. Simplify: 486y· translates to -81y² when we realize that x⁻¹ * x = x° = 1 and 486 times 1 is 486.
5. The negative sign comes from the original expression, where we had a negative base raised to an even power, which results in a positive number, but then multiplied by a negative number.

Therefore, the correct simplified form of the expression is -81y² / x². This corresponds to option (b).