How do you simplify this using the laws of exponents?

Mathematics

1 answer:

STALIN [3.7K]3 years ago

6 0

Answer:

x1 = x 61 = 6

x0 = 1 70 = 1

x-1 = 1/x 4-1 = 1/4

xmxn = xm+n x2x3 = x2+3 = x5

xm/xn = xm-n x6/x2 = x6-2 = x4

(xm)n = xmn (x2)3 = x2×3 = x6

(xy)n = xnyn (xy)3 = x3y3

(x/y)n = xn/yn (x/y)2 = x2 / y2

x-n = 1/xn x-3 = 1/x3

Step-by-step explanation:

i hope this helps if its wrong just delete my answer

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Which is the ordered pair for the point on the x-axis

mariarad [96]

The ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (-6, 10) is:

$\boxed{(6,0)}$

<h2>Explanation:</h2>

The complete question includes a graph. I have found it on the internet and has been attached below. So:

<em>To find an </em><em>ordered pair</em><em> for the point on the x-axis that is on the line parallel to the given line and through the given point (-6, 10)</em>

With two points we can get the slope of a line, so for the given linewe have the following slope (m):

$P_{1}(-8,6) \\ \\ P_{2}(4,-4) \\ \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m=\frac{-4-6}{4-(-8)} \\ \\ m=-\frac{10}{12}=-\frac{5}{6}$

Since the line we are looking for is parallel to the given line, then the slope of our unknown line (let's call it $m_{x}$ ) equals the slope of the given line. In other words:

$m_{x}=m=-\frac{5}{6}$

The point slope form of the equation of a line is:

$y-y_{0}=m(x-x_{0}) \\ \\ Where: \\ \\ P_{0}(x_{0},y_{0}) \ is \ a \ point \ on \ the \ line \\ \\ Here: \\ \\ P_{0}(-6,10) \\ \\ \\ Accordingly: \\ \\ y-10=-\frac{5}{6}(x-(-6)) \\ \\ y-10=-\frac{5}{6}(x+6)$

Finally, to find the ordered pair on the x-axis let's set $y=0$ then:

$y-10=-\frac{5}{6}(x+6) \\ \\ 0-10=-\frac{5}{6}(x+6) \\ \\ Isolating \ x: \\ \\ -\frac{5}{6}x-5=-10 \\ \\ \\ Add \ 5 \ to \ both \ sides: \\ \\ -\frac{5}{6}x-5+5=-10+5 \\ \\ -\frac{5}{6}x=-5 \\ \\ \\ Multiply \ by \ -\frac{6}{5} \ both \ sides: \\ \\ (-\frac{6}{5})(-\frac{5}{6}x)=(-5)(-\frac{6}{5}) \\ \\ \boxed{x=6}$