1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
labwork [276]
3 years ago
9

Which expression is equivalent to ( 4mn / m^-2n^6)^-2

Mathematics
1 answer:
inn [45]3 years ago
8 0

Here are a few rules with exponents that apply here:

  1. Raising a power to a power: (x^m)^n=x^{m*n}
  2. Dividing exponents of the same base: \frac{x^m}{x^n}=x^{m-n}
  3. Converting negative exponents to positive ones: x^{-m}=\frac{1}{x^m}\ \textsf{and}\ \frac{1}{x^{-m}}=x^m

Firstly, solve the outer exponent:

(\frac{4mn}{m^{-2}n^{6}})^{-2}=\frac{4^{-2}m^{-2}n^{-2}}{m^{-2*-2}n^{6*-2}}=\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}

Next, divide:

\frac{4^{-2}m^{-2}n^{-2}}{m^4n^{-12}}=4^{-2}m^{-2-4}n^{-2-(-12)}=4^{-2}m^{-6}n^{10}

Next, convert the negative exponents:

4^{-2}m^{-6}n^{10}=\frac{n^{10}}{4^2m^6}=\frac{n^{10}}{16m^6}

<u>Your final answer is n^10/16m^6 , or B.</u>

You might be interested in
If we put money in an investment that increases 14% each year . what would be the multiplier?​
matrenka [14]

Answer:

Step-by-step explanation:

1.14, just like 114%

4 0
3 years ago
Read 2 more answers
Given that 5x:9=7:3 calculate the value of x. give your answer in its simplest form.
Hitman42 [59]

\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}

<h3>x = 21/5</h3>

Step-by-step explanation:

<h3>___________________________</h3>

<h3>Given →</h3>

5x:9 = 7:3

<h3>So,</h3>

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

<h3>___________________________</h3>

<h3>Hope it helps you!!</h3>
8 0
2 years ago
A circle centered at the origin has a radius of 10 units. The terminal side of an angle, Theta, intercepts the circle in Quadran
Tanzania [10]
Since the circle is centered at the origin, we can use the equations
x² + y² = r²
x = r cos θ
y = r sin θ

We know y = 8 and r = 10. Solving for x
x² + 8² = 10²
x = 6

From this equation:
x = r cos θ
6 = 10 cos θ
cos θ = 6/10 = 0.6
7 0
3 years ago
What is 4 3/7 as a decimal.
Ymorist [56]
4.428571
I know because I googled it
4 0
3 years ago
Find the obtuse angle between the following pair of straight lines.
ioda

Given:

y=-2

y=\sqrt{3}x-1

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

y=mx+b     ...(i)

where, m is slope and b is y-intercept.

The given equations are

y=0x-2

y=\sqrt{3}x-1

On comparing these equations with (i), we get

m_1=0

m_2=\sqrt{3}

Angle between two lines whose slopes are m_1\text{ and }m_2 is

\tan \theta=\left|\dfrac{m_2-m_1}{1+m_1m_2}\right|

Putting m_1=0 and m_2=\sqrt{3}, we get

\tan \theta=\left|\dfrac{\sqrt{3}-0}{1+(0)(\sqrt{3})}\right|

\tan \theta=\left|\dfrac{\sqrt{3}}{1+0}\right|

\tan \theta=\pm \sqrt{3}

Now,

\tan \theta= \sqrt{3} and \tan \theta=-\sqrt{3}

\tan \theta= \tan 60^\circ and \tan \theta=\tan (180^\circ-60^\circ)

\theta= 60^\circ and \theta=120^\circ

120>90, so it is an obtuse angle and 60, so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.

6 0
3 years ago
Other questions:
  • 2 times the square root of 7 to the 2nd power
    13·2 answers
  • What is 1,002 in expanded form
    15·2 answers
  • Find up to isomorphism all abelian groups of order 48 72 84 g
    15·1 answer
  • A triangular field with vertices OPQ has sides OP = 402 m, PQ = 388 m, and QO = 254 m. Find the perpendicular distance from the
    13·1 answer
  • Hey can you please help me posted picture of question
    7·2 answers
  • Carlos purchased an antique chair for $56.
    9·1 answer
  • How do you find the lateral area of a pentagonal prism?
    7·1 answer
  • X/18 = (2/3)^log base x of 12
    10·1 answer
  • 2. What is the quotient of -18 divided by (- 1/6)?<br> A -108<br> С 3<br> B -3<br> D 108
    11·1 answer
  • Given f of x is equal to 2 divided by the quantity x squared plus 3x minus 10 end quantity, which of the following is true?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!