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Eduardwww [97]
3 years ago
8

Which expression is equivalent to [(3xy^-5)^3 / (x^-2y^2)^-4]^-2

Mathematics
2 answers:
True [87]3 years ago
4 0
<span>The answer is (x</span>¹⁰<span>y</span>¹⁴<span>)/729.

Explanation:
We can begin simplifying inside the innermost parentheses using the properties of exponents. The power of a power property says when you raise a power to a power, you multiply the exponents. This gives us

[(3</span>³<span>x</span>³<span>y</span>⁻¹⁵<span>)/(x</span>⁸<span>y</span>⁻⁸<span>)]</span>⁻²<span>.

Negative exponents tell us to "flip" sides of the fraction, so within the parentheses we have
[(3</span>³<span>x</span>³<span>y</span>⁸<span>)/(x</span>⁸<span>y</span>¹⁵<span>)]</span>⁻²<span>.

Using the quotient property, we subtract exponents when dividing powers, which gives us
(3</span>³<span>/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Evaluating 3</span>³<span>, we have
(27/x</span>⁵<span>y</span>⁷<span>)</span>⁻²<span>.

Using the power of a power property again, we have
27</span>⁻²<span>/x</span>⁻¹⁰<span>y</span>⁻¹⁴<span>.

Flipping the negative exponents again gives us x</span>¹⁰<span>y</span>¹⁴<span>/729.</span>
slavikrds [6]3 years ago
3 0

Answer with explanation:

The given expression is

=[\frac{(3 x y^{-5})^3}{(x^{-2}y^2)^{-4}}]^{-2}\\\\=\frac{(3 x y^{-5})^{-6}}{(x^{-2}y^2)^{8}}\\\\=\frac{(3^{-6} x^{-6} y^{30})}{(x^{-16}y^{16})}\\\\=3^{-6}\times x^{-6+16}\times y^{30-16}\\\\=\frac{x^{10}\times y^{14}}{729}

Used the following law of indices

1.[\frac{x}{y}]^m=\frac{x^m}{y^m}\\\\ 2. \frac{x^m}{x^n}=x^{m-n}\\\\ 3. \frac{1}{x^{-m}}=x^m

The given expression is equivalent to

\frac{x^{10}\times y^{14}}{729}

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Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. S
Harman [31]
ANSWER

y =  \frac{3}{2} x + 8



EXPLANATION

The line given to us has equation,

2x + 3y = 9

We need to write this equation in the slope intercept form to obtain,


3y =  - 2x + 9



\Rightarrow \: y =  -  \frac{2}{3}x + 3


The slope of this line is

m_1 =  -  \frac{2}{3}
Let the slope of the perpendicular line be

m_2

Then
m_1 \times m_2 =  - 1


-  \frac{2}{3} m_2=  - 1

This implies that,

m_2 =  - 1 \times  -  \frac{3}{2}


m_2 =  \frac{3}{2}



Let the equation of the perpendicular line be,

y = mx + b

We substitute the slope to get,


y =  \frac{3}{2} x + b

Since this line passes through
(-2,5)
it must satisfy its equation.


This means that,

5=  \frac{3}{2} ( - 2)+ b


5 =  - 3 + b



5 + 3 = b


b = 8

Wherefore the slope-intercept form is

y =  \frac{3}{2} x + 8
6 0
3 years ago
70 points!!!! Find the horizontal and the vertical components of f.
choli [55]

Answer:

  • F = (16.74, -2.95)

Explanation:

<u />

<u>1) Horizontal component</u>

The horizontal component is related to the magnitude of the force by the cosine ratio:

  • cos (α) = Fx / | F |

Where α in the angle (-10º), Fx is the horizontal component, and | F | is the magnitude of the force (17).

  • cos(-10º) = Fx / 17 ⇒ Fx = cos (-10º) × 17 = 16.74

<u />

<u>2) Vertical component</u>

The vertical component is related to the magnitude of the force by the sine ratio:

  • sin (α) = Fy / | F |

Where α in the angle (-10º), Fy is the vertical component, and | F | is the magnitude of the force (17).

  • sin(-10º) = Fy / 17 ⇒ Fy = sin (-10º) × 17 = -2.95

<u />

<u>3) Form (x,y)</u>

  • F = (16.74, -2.95)
6 0
3 years ago
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would
vitfil [10]

Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

T_A=4.225+1.375+3=8.6

The total sales tax for Florida is:

T_F=6.5+1+1.625=9.125

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

The sales tax difference in this purchase can be calculated as:

1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

ST_A=1500\cdot T_A=1500\cdot 0.086=129

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

7 0
3 years ago
Find the two numbers that have a<br> difference of 3 and a sum of 27.
polet [3.4K]
12 and 15 

15-12=3
15+12=27
5 0
2 years ago
Read 2 more answers
Sydney applied the steps below to find the product of (3.1)(–1.6).
postnew [5]

 to get the numbers in step 3

multiply -1.6 by 3

then multiply -1.6 by 0.1

 and add them together

answer is D) (–1.6)(3) + (–1.6)(0.1)

7 0
3 years ago
Read 2 more answers
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