I need to correct my test and I figured out why I missed a few of them but there are some fractions I cannot even understand how to do:
(the exponents are after a carrot and are in parentheses so there is no confusion)
14(2x)^(3)y^(5)
----------------
28x^(7)y^(3)
-3x^(-5)y^(-3)z
----------------
6x^(-3)y^(-5)z^(-2)
Sorry it's looks so confusing...
14(2x)^(3)y^(5)
---------------- =
28x^(7)y^(3)
rewriting:
14(2x)3*y5
--------------------------------- =
28x7*y3
14*8x3*y5
-------------------------------- =
28*x7y3
14 into 28 = 2 and 8/2 = 4.
4x3*y5
----------------------------- =
x7*y3
4*y5-3
------------------ =
x7-3
4y2
--------------- =
x4
I hope this looks ok and I didn't goof with the superscripts.
One trick that might help you out is to remember that powers subtract when dividing (and add when multiplying) So starting with the original equation, you can pull out all the constants (by putting them to the exponent power) then simply subtract the powers. For instance, the top half of the fraction 14 (2x)^3 * y^5 can be rewritten as 14*2^3 * x^3 * y^5 you can then just subtract the exponents on the bottom of the fraction which gives you (ignoring the constants) x^(-4) * y^(2). All that's left is dealing with the constants (which should be pretty easy) and putting the negative powers on the bottom of the fraction for the final solution.
Best of luck!
No problem! Let's break down these fractions and simplify them step by step.
For the first fraction:
14(2x)^(3)y^(5)
----------------
28x^(7)y^(3)
To simplify this, we can start by canceling out common factors in the numerator and the denominator. In this case, we can simplify both the numeric and the variable parts.
First, let's simplify the numeric part:
14 divided by 28 can be simplified to 1/2.
Now, let's simplify the variable part:
The exponent of (2x)^(3) means we need to multiply (2x) three times. So, (2x)^(3) = (2x)(2x)(2x) = 8x^(3).
Similarly, the exponent of y^(5) means we need to multiply y five times. So, y^(5) = y * y * y * y * y = y^(5).
Now, we can rewrite the fraction with the simplified parts:
(1/2)(8x^(3))y^(5)
-----------------
28x^(7)y^(3)
Next, we can cancel out common factors in the numerator and the denominator. We can cancel out an x^(3) and a y^(3):
(1/2)(8)xy^(2)
---------------
28x^(4)
Now, we can simplify this further:
4xy^(2)
-------
14x^(4)
Keep in mind that if you have additional instructions or requirements for simplifying fractions, you should follow those as well.
Moving on to the second fraction:
-3x^(-5)y^(-3)z
----------------
6x^(-3)y^(-5)z^(-2)
Let's apply the same simplification process to this fraction.
Simplifying the numeric part:
-3 divided by 6 can be simplified to -1/2.
Simplifying the variable part:
The exponent of x^(-5) means we need to divide 1 by x five times. So, x^(-5) = 1/(x * x * x * x * x) = 1/x^(5).
Similarly, the exponent of y^(-3) means we need to divide 1 by y three times. So, y^(-3) = 1/(y * y * y) = 1/y^(3).
The exponent of z^(-1) means we need to divide 1 by z. So, z^(-1) = 1/z.
Now, we can rewrite the fraction with the simplified parts:
(-1/2)(1/x^(5))(1/y^(3))(1/z)
----------------------------
6(1/x^(3))(1/y^(5))(1/z^(2))
Next, we can cancel out common factors in the numerator and denominator. We can cancel out an x^(3), a y^(3), and a z:
(-1/2)
-------
6(1/x^(2))(1/y^(2))
Simplifying further:
-1
---
12(x^(2))(y^(2))
Finally, we have simplified the second fraction to:
-1
------
12x^(2)y^(2)
Remember to always check for any additional instructions or requirements.
I hope this explanation helps you understand how to simplify fractions with exponents!