Final answer:
The expression (5x^3y^2)(+8)(6x^2) simplifies to 240x^5y^2 by multiplying the coefficients and adding the exponents of like variables.
Step-by-step explanation:
To simplify the expression (5x^3y^2)(+8)(6x^2), you need to multiply the coefficients and the variables separately. First, multiply the coefficients: 5, 8, and 6 which equals 240. Next, multiply the variables by adding the exponents of like bases according to the laws of exponents. This gives us x^(3+2)y^2, since there is only one term with a y variable, the exponent stays the same. The final simplified expression is 240x^5y^2.
Using an example for the rule of exponents, if we have (5^3)^4, it is equivalent to 5^(3*4), which is 5^12. Similarly, for the rule x^p*x^q = x^(p+q), if we have 3^2*3^5, it would simply be 3^(2+5), which is equal to 3^7.
We apply the same principle to simplify the given expression: we add the exponents of like terms and multiply the coefficients.