this is the problem: 7a(-2)power b (-4)power c (-5)power divided by 14 b(3)power c(6)power how do you simplify this

your answer is

1 divided by 2a(2)power b(12)power c(11) power

(7a-2b-4c-5)/(14b3c6)

= 1/(2a2b7c11) or
= (1/2)a-2b-7c-11)

To simplify the given expression: 7a^(-2) * b^(-4) * c^(-5) / (14 * b^3 * c^6), you can follow these steps:

Step 1: Simplify the numbers:
7 / 14 simplifies to 1/2.

Step 2: Combine the variables with the same base:
For the variables with the base "a," the exponent in the numerator is -2, while there is no power of "a" in the denominator. Therefore, "a" remains in the numerator, and its exponent remains the same (-2).

Step 3: Simplify the exponents:
For "b," the numerator has a power of -4, while the denominator has a power of +3, so you subtract the exponents: -4 - 3 = -7. The base "b" will have a negative exponent in the simplified form.

For "c," the numerator has an exponent of -5, while the denominator has an exponent of +6, so you subtract the exponents: -5 - 6 = -11. The base "c" will have a negative exponent in the simplified form.

Step 4: Arrange the simplified terms:
Now that we have simplified the expression, we can write it in its simplified form: (1/2) * a^(-2) * b^(-7) * c^(-11).

And that's the simplified form of the given expression.