I need help with a couple of math problems.
subtract 5m^2+2m+9 from 7m^2-5m-8
simplify (m^4)^3(m^2)^9/(m^3)^2
7m^2 -5m -8
5m^2 +2m +9
__________
2m^2 -7m -17
Just line up subtract the columns with different powers of m
(m^4)^3 (m^2)^9
______________
(m^3)^2
= m^12*m^18/m^6
= m^30/m^6
= ?
Just use the rules
x^a * x^b = x^(a+b)
x^a/x^b = x^(a-b)
(x^a)^b = x^(ab)
-1(m-4)2m=8
Sure, I can help you with those math problems!
1. To subtract the expression 5m^2+2m+9 from 7m^2-5m-8, we need to combine like terms. Let's break it down step by step:
Step 1: Distribute the subtraction sign to all terms in the parentheses. This means changing the signs of each term inside the parentheses:
-5m^2 - (2m) - (9)
Step 2: Combine like terms. In this case, we only have one common variable, which is 'm^2':
(7m^2 - 5m - 8) - (5m^2 + 2m + 9)
Step 3: Combine the 'm^2' terms:
7m^2 - 5m - 8 - 5m^2 - 2m - 9
Step 4: Combine the 'm' terms:
(7m^2 - 5m^2) - (5m + 2m) - (8 + 9)
Step 5: Simplify further:
2m^2 - 7m - 17
Therefore, the simplified expression is 2m^2 - 7m - 17.
2. To simplify the expression (m^4)^3(m^2)^9/(m^3)^2, we need to follow the rules of exponents. Here's how we can break it down:
Step 1: Apply the exponent rule for raising a power to a power. Multiply the exponents within each base:
m^(4*3) * m^(2*9) / m^(3*2)
Simplified:
m^12 * m^18 / m^6
Step 2: Apply the exponent rule for dividing powers with the same base. Subtract the exponents:
m^(12+18-6)
Simplified:
m^24
Therefore, the simplified expression is m^24.