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
2m=p-q/r solve for r
Oduvanchick [21]

To solve for r, you would start by subtracting p from both sides.

2m - p = -q/r

Multiply everything by r.

2mr - pr = -q

Factor r out of the left side of the equation.

r(2m - p) = -q

Divide both sides by (2m - p).

r = \frac{-q}{2m-p} = \frac{q}{2m + p}.

6 0
3 years ago
Which color is the line that represents an equivalent ratio? How can you tell by looking at the lines? A) blue; The graph is a v
Genrish500 [490]

Answer:

C) pink; The graph of the pink line passes through the origin.

6 0
3 years ago
PLEASE HELP ME IM BAD AT GEO! URGENT
cupoosta [38]

Answer:

SSS

Step-by-step explanation:

Given that the sides are equal and no angles are given

6 0
3 years ago
Read 2 more answers
How to make 100 using 5 digits
madam [21]
10*5+10*5*1 I think this is the right way
8 0
3 years ago
What is the equation I'm supposed to write?
wolverine [178]

The equation in slope intercept form is y = -4x/3 + 10

<h3>How to determine the equation?</h3>

The representations are given as:

  • x represents peaches
  • y represents apples

So, we have:

2 * x + 1.5 * y = 15

Evaluate the product

2x + 1.5y = 15

Subtract 2x from both sides

1.5y = -2x + 15

Divide through by 1.5

y = -4x/3 + 10

Hence, the equation in slope intercept form is y = -4x/3 + 10

Read more about linear equations at:

brainly.com/question/14323743

#SPJ1

8 0
2 years ago
Other questions:
  • A triangle can be formed with side lengths 3 in, 5 in, and 9 in.<br><br> True<br> False
    9·2 answers
  • The volume of a cone-shaped dessert is 10 CUBIC CENTIMETRES.
    15·1 answer
  • Cuál es el mejor estimado para la suma de 3/8 y 1/12
    13·1 answer
  • Round 5,112 to the nearest thossand
    5·2 answers
  • Find the common ratio of the geometric sequence: 12.5,−62.5,312.5,−1562.5,… A. 5 B. -5 C. −15 D. 15
    11·1 answer
  • How much longer is the big arc than the small arc. Give the answer to 1 decimal place
    12·1 answer
  • Choose the single logarithmic expression that is equivalent to the one shown. 2log4 +log2 + log2
    6·1 answer
  • On a set of blueprints for a new home, the contractor has established a scale of 0.5in : 10 ft. What are the dimensions on the b
    14·1 answer
  • Every integer number is also a. Irrational number b. Whole number c. Natural number d. Rational number
    11·1 answer
  • . A pedestal is built using a trapezoid-shaped base. Find the area of the trapezoid.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!