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
Everything is done but the last step, please help, thanks
If no math tutor comes online who can help you, you should see if you can find explanations here:
http://www.khanacademy.org/
There is no need to connect with Facebook or anything. Just scroll down to the Math section (just under BROWSE OUR LIBRARY) and find the math level you're studying. Once you're in the right section, go through the videos in which different math concepts are taught.
Make sure you don't just sit around here waiting for someone to show up!!
Here are other websites that may have explanations to help:
http://www.aaamath.com/
http://mathforum.org/dr.math/
Not sure what it is you want to do. What is the "last step"? The "big numbers" are just coefficients, and can be moved around as needed, since multiplication is commutative.
x^2(xy)^3: x2(x^3y^3): x^5y^3
3x^2(2x)^3: 3x^2 (8x^3): 3x^2 * 8x^3: 24x^5
-2x^2y(3xy^2)^2: (-2)(x^2y)(9)(x^2y^4): -18x^4y^5
-(3x)^2: -(9x^2): (-1)(9x^2): (-1)(9)x^2: -9x^2
5x(2x^2)^2: (5)(x)(4x^4): 20x^5
-3x^2y(xy)^3: -3x^5y^4
2xy^2(3x^2y)^3: 54x^7y^5
One thing they didn't test was things like
(-3xy^2)^2: (-3)^2 x^2y^4: 9x^2y^4
having a "-" inside the parens can make a difference!
To simplify these expressions, you need to follow the order of operations which states that you should perform any operations inside parentheses first, then apply exponentiation, and finally perform multiplication or division from left to right.
Let's go through each expression step by step:
1. x^2(xy)^3: x2(x^3y^3)
To simplify this expression, you first need to apply the exponent to the term inside the parentheses: (xy)^3 = x^3y^3. Then, you multiply the resulting term by x^2: x^2(x^3y^3) = x^(2+3)y^3 = x^5y^3.
2. 3x^2(2x)^3: 3x^2 (8x^3)
In this expression, you need to apply the exponent to the term inside the parentheses: (2x)^3 = 8x^3. Then, multiply the resulting term by 3x^2: 3x^2(8x^3) = 24x^(2+3) = 24x^5.
3. -2x^2y(3xy^2)^2
Start by calculating the exponentiation inside the parentheses: (3xy^2)^2 = 9x^2y^4. Then, multiply the resulting term by -2x^2y: -2x^2y(9x^2y^4) = -18x^(2+2)y^(1+4) = -18x^4y^5.
4. -(3x)^2: -(9x^2)
Here, you apply the exponent to the term inside the parentheses: (3x)^2 = 9x^2. Then, you simply add the negative sign: -(9x^2) = -9x^2.
5. 5x(2x^2)^2
Calculate the exponentiation inside the parentheses: (2x^2)^2 = 4x^4. Then, multiply the resulting term by 5x: 5x(4x^4) = 20x^(1+4) = 20x^5.
6. -3x^2y(xy)^3
First, calculate the exponent inside the parentheses: (xy)^3 = x^3y^3. Then, multiply the resulting term by -3x^2y: -3x^2y(x^3y^3) = -3x^(2+3)y^(1+3) = -3x^5y^4.
7. 2xy^2(3x^2y)^3
Start by calculating the exponentiation inside the parentheses: (3x^2y)^3 = 27x^6y^3. Next, multiply the resulting term by 2xy^2: 2xy^2(27x^6y^3) = 54x^(1+6)y^(2+3) = 54x^7y^5.
Each of these steps follows the order of operations and simplifies the expression. Make sure to check your work to avoid any mistakes.