(4a*2)(5a*−1)*2(7b*3)(5b*−2)
wrong again!
(4a^2)(5a^−1)^2 (7b^3)(5b^−2)
= 4a^2 * (5/a)^2 * 7b^3 * 5/b^2
= 4a^2 * 25/a^2 * 7b^3 * 5/b^2
= 4*25*7*5 b
= 3500b
Apologies for the previous incorrect response. You are absolutely right.
The simplified expression is indeed:
3500b
To simplify the given expression: (4a*2)(5a*−1)*2(7b*3)(5b*−2), we'll start by using the properties of exponents.
First, let's simplify each term inside the parentheses individually:
1. (4a*2) = 4 * a^2
2. (5a*−1) = 5 * a^-1
3. (7b*3) = 7 * b^3
4. (5b*−2) = 5 * b^-2
Now, we can rewrite the expression by substituting these simplified terms:
(4 * a^2)(5 * a^-1) * 2 * (7 * b^3)(5 * b^-2)
Next, we can simplify further by multiplying the coefficients and combining the variables with the same base:
4 * 5 * 2 * 7 * a^2 * a^-1 * b^3 * 5 * b^-2
Multiplying the coefficients: 4 * 5 * 2 * 7 * 5 = 2800
Combining the variables: a^2 * a^-1 = a^(2 - 1) = a^1 = a and b^3 * b^-2 = b^(3 - 2) = b^1 = b
So, the simplified expression is 2800 * a * b.
First, let's simplify each term within parentheses:
(4a*2) simplifies to 4a^2.
(5a*−1) simplifies to 5/a.
(7b*3) simplifies to 7b^3.
(5b*−2) simplifies to 5/b^2.
Now, plug in these simplified terms into the original expression:
(4a^2)(5/a)*2(7b^3)(5/b^2)
Multiplying the coefficients:
(4*5)*(2*7) = 20*14 = 280
Multiplying the variables with the same base and adding exponents:
a^2 * a^(-1) = a^(2+(-1)) = a^1 = a
b^3 * b^(-2) = b^(3+(-2)) = b^1 = b
Plugging in these simplified exponents:
280a*2*b
Multiplying the coefficients:
280*2 = 560
The final simplified expression is:
560a*b