Question

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

A. 8b12a9
B. quantity 8 times b raised to the twelfth power end quantity over a raised to the ninth power
C. 1 over quantity 6 times a raised to the ninth power times b raised to the twelfth power end quantity
D. 1 over quantity 8 times a raised to the ninth power times b raised to the twelfth power end quantity

Answer 1

To simplify a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed, you apply the exponent to both the 2 and b to the fourth power and handle the negative exponent on a to find that the simplified expression is 1 over the product of 8, a raised to the ninth power, and b raised to the twelfth power. Option D.

Step-by-step explanation:

The task is to simplify the expression a-3 / (2b4)3.

First, when an exponent is applied to a product inside parentheses, we apply the exponent to both terms inside.

Thus, (2b4)3 becomes 23b4*3 which is 8b12.

Now, we must handle the negative exponent on a. A negative exponent indicates that you take the reciprocal of the base and make the exponent positive, so a-3 becomes 1/a3.

When you cube the term that's being divided (as in a-3), you also cube the exponent, resulting in 1/a9.

Combining the two steps, we get (1/a9) / (8b12), and when you divide by a fraction, you multiply by its reciprocal: 1 / (8a9b12).

The correct answer is option D. 1 over quantity 8 times a raised to the ninth power times b raised to the twelfth power end quantity.

Answer 2

The simplification of the given expression a^(-3) / (2b^4)^3 is option D 1 / (8a^3 * b^12).

The given expression is a^(-3) / (2b^4)^3.

To simplify this, we first deal with the exponent outside the parentheses. Since a^(-3) is in the denominator, we can rewrite it as 1/a^3.

Now, inside the parentheses, we have (2b^4)^3 which equals 8b^12 (since 2^3 = 8 and (b^4)^3 = b^(4*3) = b^12).

So, our expression becomes 1/a^3 * 1/(8b^12).

Combining these fractions gives us 1 / (8a^3 * b^12), which can be written as option D: 1 over quantity 8 times a raised to the ninth power times b raised to the twelfth power end quantity. Therefore, option D is the correct answer.