Question

Which expression is equivalent to (4g^3h^2k^4) / 8g^3h^2 - (h^5k^3)^5?

Answer 1

To simplify the given expression, start by canceling out common terms in the numerator and denominator. Then, divide the numerator by the denominator by subtracting the exponents of the common base. The simplified expression is 4k^(-11).

Step-by-step explanation:

To simplify the expression (4g^3h^2k^4) / 8g^3h^2 - (h^5k^3)^5, let's break it down step by step:

1. First, simplify the numerator by canceling out common terms. We can cancel out g^3h^2 in the numerator and denominator, leaving us with 4k^4.
2. Next, simplify the denominator by expanding (h^5k^3)^5. This gives us h^25k^15.
3. Now, divide the numerator 4k^4 by the denominator h^25k^15. To do this, we subtract the exponents of the common base k. This gives us 4k^(4-15) which simplifies to 4k^(-11).

So, the simplified expression is 4k^(-11).