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Alenkinab [10]
3 years ago
14

I need help on doing (2a^-6 b^4)^3 • 2a^-3 b^-5?

Mathematics
1 answer:
aev [14]3 years ago
3 0
<h2>Steps</h2>

So here are a few rules with exponents that we will be applying for this problem:

  • Powering a power: (x^m)^n=x^{m*n}
  • Multiplying powers with the same base: x^m*x^n=x^{m+n}
  • Converting negative exponents to positive exponents: x^{-m}=\frac{1}{m^n}\ \textsf{//}\ \frac{1}{x^{-m}}=x^m

Firstly, solve the outermost power:

(2a^{-6} b^4)^3*2a^{-3} b^{-5}\\2^3a^{-6*3} b^{4*3}*2a^{-3} b^{-5}\\8a^{-18}b^{12}*2a^{-3}b^{-5}

Next, multiply:

8a^{-18}b^{12}*2a^{-3}b^{-5}\\8*2a^{-18+(-3)}b^{12+(-5)}\\16a^{-21}b^7

Finally, convert the negative exponents:

16a^{-21}b^7\\\\\frac{16b^7}{a^{21}}

<h2>Answer</h2>

<u>In short, your final answer is \frac{16b^7}{a^{21}}</u>

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Step-by-step explanation:

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Misha Larkins [42]

Given :

Center of sphere , C( 1 , -1 , 6 ) .

To Find :

Find equations of the spheres with center (1, −1, 6) that touch the following planes.a) xy-plane b) yz-plane c) xz-plane .

Solution :

a)

Distance of the point from xy-plane is :

d = 6 units .

So , equation of circle with center C and radius 6 units is :

(x-1)^2+(y-(-1))^2+(z-6)^2=6^2\\\\(x-1)^2+(y+1)^2+(z-6)^2=36

b)

Distance of point from yz-plane is :

d = 1 unit .

So , equation of circle with center C and radius 1 units is :

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c)

Distance of point from xz-plane is :

d = 1 unit .

So , equation of circle with center C and radius 1 units is :

(x-1)^2+(x+1)^2+(z-6)^2=1^2\\\\(x-1)^2+(x+1)^2+(z-6)^2=1

Hence , this is the required solution .

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3 years ago
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Slope is rise/run
so, you go up 4 times and run across 3 times, this is a positive slope, so the slope is
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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

The equation of the line in point-slope form is given as

y-y_1=m(x-x_1)

Here m=-3 and (x1, y1)=(5, 9)

Therefore,

y-9=-3(x-5)

8 0
3 years ago
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