What are your options for the questions.
because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.
By distributing the power of 2, we will get y^2(6).
Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.
summary:
multiply exponents if they are being raised to a power.
add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)
By simplifying
. This will result in a simplified version of
.
The Simplifying Algorithm is a wonderful way to simplify complex mathematics problems. It can be used to solve equations, convert fractions to decimals, and perform many other math operations. In this problem, the Simplifying Algorithm will help you reduce ![\[x - \frac{{23}}{{{x^2}}} - x - 20 - \frac{2}{5} - x\]](https://tex.z-dn.net/?f=%5C%5Bx%20-%20%5Cfrac%7B%7B23%7D%7D%7B%7B%7Bx%5E2%7D%7D%7D%20-%20x%20-%2020%20-%20%5Cfrac%7B2%7D%7B5%7D%20-%20x%5C%5D)
Since two opposites add up to 0, remove them from the expression.
![\[ - \frac{{23}}{{{x^2}}} - \frac{{102}}{5} - x\]](https://tex.z-dn.net/?f=%5C%5B%20-%20%5Cfrac%7B%7B23%7D%7D%7B%7B%7Bx%5E2%7D%7D%7D%20-%20%5Cfrac%7B%7B102%7D%7D%7B5%7D%20-%20x%5C%5D)
Write all numerators above the least common denominator 5x2
![\[ - \frac{{115 + 102{x^2} + 5{x^3}}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%20-%20%5Cfrac%7B%7B115%20%2B%20102%7Bx%5E2%7D%20%2B%205%7Bx%5E3%7D%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
Use the commutative property to reorder the terms so that constants on the left
![\[\frac{{ - 5{x^3} - 115 - 102{x^2}}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B%7B%20-%205%7Bx%5E3%7D%20-%20115%20-%20102%7Bx%5E2%7D%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
Rearrange the terms
![\[\frac{{ - 5{x^3} - 102{x^2} - 115}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B%7B%20-%205%7Bx%5E3%7D%20-%20102%7Bx%5E2%7D%20-%20115%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
By reording the terms
![\[ - \frac{{5{x^3} + 102{x^2} + 115}}{{5{x^2}}}\]](https://tex.z-dn.net/?f=%5C%5B%20-%20%5Cfrac%7B%7B5%7Bx%5E3%7D%20%2B%20102%7Bx%5E2%7D%20%2B%20115%7D%7D%7B%7B5%7Bx%5E2%7D%7D%7D%5C%5D)
Hence, by simplifying this equation, divide both numerator and denominator. This will result in a simplified version of
.
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Cos theta = base /perp
= sqrt(13)/7
=0.515