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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>

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Kruka [31]

Answer:

i think its 18 :))

8 0
3 years ago
Ricky Bobby wants to buy a new automobile for $55,000 in 8 years. How much money must Ricky's original investment be if he makes
laila [671]

Answer:

PV= $40,279.36

Step-by-step explanation:

Giving the following information:

Number of periods= 8*12= 96 months

Interest rate= 0.039/12= 0.00325

Future value (PV)= $55,000

<u>To calculate the initial investment, we need to use the following formula:</u>

PV= FV/(1+i)^n

PV= 55,000 / (1.00325^96)

PV= $40,279.36

4 0
3 years ago
What is the unit rate of this question
kykrilka [37]
Answer: 64 mph

We can see that after every hour, the car has traveled 64 miles. So the speed rate is 64 miles per hour.
8 0
3 years ago
Read 2 more answers
What is 8.57x10-⁴ in standered form ?
marusya05 [52]

Kaleerain5,

In order to get your answer you must remember that if the exponent is negative move to the left and if the exponent is positive you have to move to the right.

  • 8.57 \times 10^{-4}
  • The exponent is negative so move to the left:
  • 8. = .8 = .08 = .008 = .0008
  • = .000857

Therefore your answer is ".000857."

Hope this helps!

6 0
3 years ago
Wen was hiking on a 12-mile route. During the first 2 hours, his hiking speed was 3 mph. During the rest of the hike, his speed
Mars2501 [29]

The total time taken to cover 12 miles distance is 5 hours.

<u>Given the Parameters</u> :

  • Total distance hiked = 12 miles

Recall :

  • Distance = speed × time

Let :

  • Total Time taken = t

<u>We could create an equation thus</u> :

Total distance = 3(2) + 2(t - 2)

12 = 6 + 2t - 4

12 = 2 + 2t

12 - 2 = 2t

10 = 2t

t = 10/2

t = 5

Therefore, the total time taken is 5 hours

Learn more :brainly.com/question/18796573

5 0
2 years ago
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