How would I solve this equation?
-11p^6r^4
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(-2p^4)^3 (-10p^5r^4)
To solve this equation, you need to simplify the expression by performing the calculations and simplifications step-by-step. Let's break it down:
Step 1: Simplify the numerator expression.
The numerator is -11p^6r^4. Since there are no like terms, we can't simplify it further.
Step 2: Simplify the denominator expression.
The denominator is (-2p^4)^3 (-10p^5r^4). We can simplify it as follows:
(-2p^4)^3 = (-2)^3 (p^4)^3 = -8p^12
Thus, the denominator simplifies to -8p^12 (-10p^5r^4).
Step 3: Rewrite the equation with the simplified expressions.
The equation becomes:
-11p^6r^4 / -8p^12 (-10p^5r^4)
Step 4: Simplify further if possible.
Keep in mind that when dividing by a fraction, multiplying by its reciprocal is a more straightforward approach. Let's flip the denominator and multiply instead:
-11p^6r^4 * (-10p^5r^4) / -8p^12
Step 5: Combine like terms and simplify the expression further.
When multiplying, you can combine like terms by adding or subtracting the exponents with the same base (in this case, p and r).
-11 * -10 = 110
p^6 * p^5 = p^(6+5) = p^11
r^4 * r^4 = r^(4+4) = r^8
Our equation becomes:
110p^11r^8 / -8p^12
Step 6: Simplify if possible.
We can simplify further by dividing the coefficients and subtracting the exponents. Since p^11/p^12 = 1/p and the signs in the numerator and denominator are different, we get:
-110/8p (r^8)
So, the simplified equation is:
-110/8p (r^8)