simplify:
(2x^2y)(-5x^-5y^6)
(5y)^3
I noticed this question before, did not answer it because I thought it was ambigious.
Are there two different problems here or is it one continuous multiplication.
I will assume you have
(2x^2y)(-5x^-5y^6) which is
= -10x^-3y^7
or
= -10y^7/x^3
(5y)^3 = 125y^3
not much was gained in "simplification" here.
yes they were two different problems and yes i know they're stupid questions in my math book.
To simplify the expressions, let's use the rules of exponents and multiplication.
For the first expression, (2x^2y)(-5x^-5y^6), we can simplify by multiplying the coefficients (numbers in front of the variables) and adding the exponents.
Step 1: Multiply the coefficients: 2 * -5 = -10.
Step 2: Simplify the x-terms by adding the exponents: x^2 * x^-5 = x^2 + (-5) = x^(-3) (Remember, when you multiply with the same base, you add the exponents).
Step 3: Simplify the y-terms by adding the exponents: y * y^6 = y^1 * y^6 = y^(1+6) = y^7.
Putting it all together, we have -10x^(-3)y^7 as the simplified expression.
For the second expression, (5y)^3, we can simplify by using the power rule of exponents.
The power rule states that when a power is raised to another power, you multiply the exponents. In this case, we have (5y)^3, which is equivalent to (5^1 * y^1)^3.
Step 1: Apply the power rule by multiplying the exponents: 5^1 * y^1 * 3 = 5^(1*3) * y^(1*3) = 5^3 * y^3.
Step 2: Simplify the expression: 5^3 = 5 * 5 * 5 = 125.
So, the simplified expression (5y)^3 is equal to 125y^3.