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
Please help, thanks !!!
To simplify these expressions, you need to follow the order of operations, which is commonly known as PEMDAS. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Let's go through each question step by step:
1. x^2(xy)^3: x2(x^3y^3)
To simplify this expression, you need to apply the exponent rule first. The exponent rule states that when you raise a power to another power, you multiply the exponents. So, we have:
(x^2) * (x^3y^3)
This simplifies to:
x^(2 + 3)y^3
Now, you add the exponents of x, which gives you:
x^5y^3
2. 3x^2(2x)^3: 3x^2(8x^3)
Here, you need to first calculate the exponent of (2x)^3, which is 8x^3. Now, you have:
3x^2 * 8x^3
When you multiply two terms with the same base (in this case, x), you add the exponents. So, we get:
24x^(2+3)
This simplifies to:
24x^5
3. -2x^2y(3xy^2)^2
First, calculate the exponent of (3xy^2)^2, which gives you 9x^2y^4. Now, you have:
-2x^2y * 9x^2y^4
When you multiply two terms with the same base, you add the exponents. So, we get:
-18x^(2+2)y^(1+4)
This simplifies to:
-18x^4y^5
4. -(3x)^2: -(9x^2)
To simplify this expression, you need to calculate the exponent. (3x)^2 is equivalent to (3x)(3x), which is 9x^2. Now, we have:
-(9x^2)
There are no like terms to add or subtract, so this expression cannot be simplified any further.
5. 5x(2x^2)^2
First, simplify the exponent of (2x^2)^2, which gives you 4x^4. Now, you have:
5x * 4x^4
When you multiply two terms with the same base, you add the exponents. So, we get:
20x^(1+4)
This simplifies to:
20x^5
6. -3x^2y(xy)^3
First, calculate the exponent of (xy)^3, which gives you x^3y^3. Now, you have:
-3x^2y * x^3y^3
When you multiply two terms with the same base, you add the exponents. So, we get:
-3x^(2+3)y^(1+3)
This simplifies to:
-3x^5y^4
7. 2xy^2(3x^2y)^3
First, calculate the exponent of (3x^2y)^3, which gives you 27x^6y^3. Now, you have:
2xy^2 * 27x^6y^3
When you multiply two terms with the same base, you add the exponents. So, we get:
54x^(1+6)y^(2+3)
This simplifies to:
54x^7y^5
Remember, always make sure to apply the exponent rules and simplify each term before combining like terms.