How do you do these questions, I have all my steps done until the last one:
2x(2x)^2: 2x(4x^2)?
Now do I multiply or add the big numbers?
also Im having trouble on these:
1. x^2(xy)^3: x2(x^3y^3)
2. 3x^2(2x)^3: 3x^2 (8x^3)
3. -2x^2y(3xy^2)^2
4. -(3x)^2: -(9x^2)?
5. 5x(2x^2)^2
6. -3x^2y(xy)^3
7. 2xy^2(3x^2y)^3
Everythinbg is done but the last step, please help, thanks
To simplify these expressions, you need to follow the order of operations, which is typically remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
1. x^2(xy)^3: x2(x^3y^3)
First, apply the exponent to xy: (xy)^3 equals x^3y^3.
Then, you can distribute x^2 to both terms in the expression: x^2 * x^3y^3 = x^(2+3)y^3 = x^5y^3.
2. 3x^2(2x)^3: 3x^2(8x^3)
Start by calculating the exponent of (2x)^3: (2x)^3 equals 8x^3.
Then simply multiply 3x^2 by 8x^3: 3x^2 * 8x^3 = 24x^(2+3) = 24x^5.
3. -2x^2y(3xy^2)^2
Begin by simplifying the expression inside the parentheses: (3xy^2)^2 equals 9x^2y^4.
Multiply this by -2x^2y: -2x^2y * 9x^2y^4 = -18x^(2+2)y^(1+4) = -18x^4y^5.
4. -(3x)^2: -(9x^2)
Apply the exponent to (3x)^2: (3x)^2 equals 9x^2.
Then, multiply this by -1: -(9x^2).
5. 5x(2x^2)^2
First calculate the exponent inside the parentheses: (2x^2)^2 equals 4x^4.
Multiply 5x by 4x^4: 5x * 4x^4 = 20x^(1+4) = 20x^5.
6. -3x^2y(xy)^3
Simplify the exponent inside the parentheses: (xy)^3 equals x^3y^3.
Multiply -3x^2y by x^3y^3: -3x^2y * x^3y^3 = -3x^(2+3)y^(1+3) = -3x^5y^4.
7. 2xy^2(3x^2y)^3
Calculate the exponent of (3x^2y)^3: (3x^2y)^3 equals 27x^6y^3.
Multiply 2xy^2 by 27x^6y^3: 2xy^2 * 27x^6y^3 = 54x^(1+6)y^(2+3) = 54x^7y^5.
Remember to apply the proper exponent rules and distribute when necessary.