(5x ^3)2(2x^7)
To simplify the expression (5x^3)^2(2x^7), you need to apply the rules of exponents and the multiplication of powers.
Step 1: Simplify the expression inside the first set of parentheses: (5x^3)^2.
To square a binomial, you multiply it by itself. In this case, (5x^3)^2 = 5^2 * (x^3)^2.
Step 2: Apply the rule of exponents for the base 5: 5^2 = 25.
Step 3: Apply the rule of exponents for the base x^3: (x^3)^2 = x^(3*2) = x^6.
After simplifying the first set of parentheses, the expression becomes:
25 * x^6 * (2x^7).
Step 4: Multiply the coefficients (25 and 2) together: 25 * 2 = 50.
Step 5: Multiply the variable parts (x^6 and x^7) together using the rule of exponents for multiplication: x^6 * x^7 = x^(6 + 7) = x^13.
Putting it all together, the simplified expression is:
50 * x^13.