How do you do these questions, I have all my steps 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 rules of exponentiation and use the properties of multiplication.
1. x^2(xy)^3: To simplify this expression, you need to apply the power of a product rule. Raise both the x and y to the power of 3:
x^2(xy)^3 = x^2(x^3y^3)
Now you can simplify this expression. Multiply the powers of x and y:
x^2(x^3y^3) = x^(2+3)y^(3)
The final simplified expression is x^5y^3.
2. 3x^2(2x)^3: To simplify this expression, use the power of a power rule. Raise both the 2x and the exponent 3:
3x^2(2x)^3 = 3x^2(2^3x^3)
Simplify the expression inside the parentheses first:
3x^2(2^3x^3) = 3x^2(8x^3)
Now, multiply the coefficients and add the exponents of x:
3x^2(8x^3) = 24x^5
The final simplified expression is 24x^5.
3. -2x^2y(3xy^2)^2: To simplify this expression, apply the power of a product rule. Square the expression inside the parentheses:
-2x^2y(3xy^2)^2 = -2x^2y(3^2x^2y^4)
Simplify the expression inside the parentheses first:
-2x^2y(3^2x^2y^4) = -2x^2y(9x^2y^4)
Multiply the coefficients and add the exponents of x and y:
-2x^2y(9x^2y^4) = -18x^4y^5
The final simplified expression is -18x^4y^5.
4. -(3x)^2: To simplify this expression, apply the power of a product rule. Square the expression inside the parentheses:
-(3x)^2 = -1(3^2x^2)
Simplify the expression inside the parentheses:
-1(3^2x^2) = -1(9x^2)
The final simplified expression is -9x^2.
5. 5x(2x^2)^2: To simplify this expression, apply the power of a power rule. Raise both the 2x^2 and the exponent 2:
5x(2x^2)^2 = 5x(4x^4)
Multiply the coefficients and add the exponents of x:
5x(4x^4) = 20x^5
The final simplified expression is 20x^5.
6. -3x^2y(xy)^3: To simplify this expression, apply the power of a product rule. Raise both the xy and the exponent 3:
-3x^2y(xy)^3 = -3x^2y(x^3y^3)
Multiply the coefficients and add the exponents of x and y:
-3x^2y(x^3y^3) = -3x^5y^4
The final simplified expression is -3x^5y^4.
7. 2xy^2(3x^2y)^3: To simplify this expression, apply the power of a product rule. Raise both the 3x^2y and the exponent 3:
2xy^2(3x^2y)^3 = 2xy^2(27x^6y^3)
Multiply the coefficients and add the exponents of x and y:
2xy^2(27x^6y^3) = 54x^7y^5
The final simplified expression is 54x^7y^5.