What are the product of these using the laws of exponent?
(ab²) (a3b²) (-ab3) =
12m4n4
______ =
12m4n4
33x²y.-9xy² =
9a²b.3ab3.2ab =
What do you get?
Note a^4 = a to the fourth power
12 a = 12*a = twelve times a
a^n * a^m = a^(m+n)
a^n/a^m = a^(n-m)
To find the product of the given expressions using the laws of exponents, we need to apply the rules for multiplying variables with exponents:
1. (ab²) * (a³b²) * (-ab³):
- Multiply the coefficients: 1 * 1 * (-1) = -1.
- Multiply the variables with the same base (a) and add the exponents: a^(1+3-1) = a³.
- Multiply the variables with the same base (b) and add the exponents: b^(2+2-3) = b¹.
- Putting it all together, the product is -a³b.
2. 33x²y * (-9xy²):
- Multiply the coefficients: 33 * (-9) = -297.
- Multiply the variables with the same base (x) and add the exponents: x^(2+1) = x³.
- Multiply the variables with the same base (y) and add the exponents: y^(1+2) = y³.
- Putting it all together, the product is -297x³y³.
3. 9a²b * 3ab³ * 2ab:
- Multiply the coefficients: 9 * 3 * 2 = 54.
- Multiply the variables with the same base (a) and add the exponents: a^(2+1+1) = a⁴.
- Multiply the variables with the same base (b) and add the exponents: b^(1+3+1) = b⁵.
- Putting it all together, the product is 54a⁴b⁵.
Therefore, the expressions simplify to:
1. -a³b
2. -297x³y³
3. 54a⁴b⁵