can you tell me the process of how to simply problems like this so i don't have to keep asking?
simplify:
(2x^2y)(-5x^-5y^6)
(5y)^3
Certainly! I'd be happy to explain how to simplify these expressions.
To simplify the expression (2x^2y)(-5x^-5y^6), you can start by multiplying the coefficients (numbers) together and then combine the variables with the same base. Here's the step-by-step process:
1. Multiply the coefficients: 2 x -5 = -10.
2. Multiply the variables with the same base separately. For the x-terms, multiply the exponents: x^2 * x^-5 = x^(2 + -5) = x^(-3). Remember that when multiplying variables with the same base, you add the exponents.
3. For the y-terms, multiply the exponents: y^1 * y^6 = y^(1 + 6) = y^7.
Putting it all together, the simplified expression is -10x^(-3)y^7.
Now, let's move on to simplifying (5y)^3.
To simplify the expression (5y)^3, you need to raise both the coefficient and the variable to the power of 3. Here's how:
1. Raise the coefficient to the power of 3: 5^3 = 5 * 5 * 5 = 125.
2. Raise the variable, y, to the power of 3: y^3.
Combining the coefficient and the variable, the simplified expression is 125y^3.
Remember, when simplifying expressions, it's important to understand the rules of exponents and apply them accordingly.