1. Simplify the expression: (x^3*y^5) (-y^7)
2. Write the expression in radical form: (125x)^1/3
1. To simplify the expression (x^3 * y^5) * (-y^7), we can use the rules of exponents.
First, multiply the coefficients (which in this case is just 1) and get 1 * 1 = 1.
Next, for the x terms, we add the exponents when multiplying with the same base. So we have x^3 * x^0 = x^(3 + 0) = x^3.
For the y terms, we subtract the exponents when dividing with the same base. Here we have y^5 * y^7 = y^(5 + 7) = y^12.
Finally, we combine the x and y terms, giving us the simplified expression 1 * x^3 * y^12 = x^3 * y^12.
2. To write the expression (125x)^(1/3) in radical form, we need to determine the cube root of 125x.
The cube root symbol (∛) indicates finding the number (or expression) that, when cubed, gives the original number (or expression).
First, we evaluate the cube root of 125:
∛125 = 5, since 5 * 5 * 5 = 125.
Next, we evaluate the cube root of x:
∛x = x^(1/3).
Thus, the expression (125x)^(1/3) can be written as 5 * x^(1/3), which is the radical form.