Question

Simplify a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed.

8b12a9
quantity 8 times b raised to the twelfth power end quantity over a raised to the ninth power
1 over quantity 6 times a raised to the ninth power times b raised to the twelfth power end quantity
1 over quantity 8 times a raised to the ninth power times b raised to the twelfth power end quantity

Answer 1

Answer:To simplify the expression "a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed", we can follow these steps:

Step 1: Simplify the numerator.

a raised to the negative third power is equivalent to 1 over a cubed.

Step 2: Simplify the denominator.

2 times b raised to the fourth power is equivalent to 2b to the fourth power.

Step 3: Combine the simplified numerator and denominator.

So, the expression becomes 1 over a cubed divided by 2b to the fourth power, all cubed.

Step 4: Simplify the division.

When we divide by a fraction, we can multiply by its reciprocal.

The reciprocal of 2b to the fourth power is 1 over 2b to the fourth power.

Therefore, the expression simplifies to 1 over a cubed times 1 over the reciprocal of 2b to the fourth power, which is 1 over 2b to the fourth power.

In summary, the simplified expression is 1 over 2b to the fourth power times a cubed.

Answer 2

`(1)/(8a^9b^12)`

Explanation:

`((a^(-3))/(2b^4))^3 =`

`= ((1)/(2a^3b^4))^3`

`= (1)/(8a^9b^(12))`