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Nostrana [21]
3 years ago
8

Why do you subtract exponents when dividing powers with the same base?

Mathematics
1 answer:
enyata [817]3 years ago
5 0

Because the factors in the numerator cancel with the factors in the denominator. Consider this example:

\dfrac{6^7}{6^4} = \dfrac{6\times6\times6\times6\times6\times6\times6}{6\times6\times6\times6} = 6\times6\times6 = 6^3 = 6^{7-4}

All of the 6's in the denominator canceled with the 6's in the numerator, and only 3 6's "survived". The opposite can also happen, if there are more terms in the denominator:

\dfrac{2^2}{2^4} = \dfrac{2\times 2}{2\times 2\times 2 \times 2} = \dfrac{1}{2^2} = 2^{-2} = 2^{2-4}

So, everything is coherent

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You are paid $82.50 for 71212 hours of work. What is your rate of pay?
yanalaym [24]
If you would like to know what is your rate of pay, you can calculate this using the following steps:

$82.50 ... 7.5 hours
$x = ? ... 1 hour

82.50 * 1 = 7.5 * x
82.50 = 7.5 * x     /7.5
x = 82.50 / 7.5
x = $11

The correct result would be $11 per hour.
3 0
4 years ago
What is the explicit formula for the arithmetic sequence -100,-70,-40,-10
kherson [118]

The explicit formula of an arithmetic sequence:

a_n=a_1+(n-1)d

We have:

a_1=-100,\ a_2=-70,\ a_3=-40;\ a_4=-10,\ ...\\\\d=a_{n+1}-a_n\to d=-70-(-100)=-70+100=30

Substitute:

a_n=-100+(n-1)(30)=-100+30n-30=30n-130

Answer: an = 30n - 130

7 0
3 years ago
Which mixed number shows the result of 671 divided by 83
djverab [1.8K]

Answer:

8 7/83

Step-by-step explanation:

671/83

8.084= 8 7/83

3 0
3 years ago
Michael has a pail that holds 5 gallons of
damaskus [11]

Answer:

20 quarts.

Step-by-step explanation:

Because there are 20 quarts in 5 gallons.

5 0
3 years ago
Bobbys collection of sports cards has 3/10 baseBall cards and 39/100 foo taller cards. THe rest are soccer cards. What fraction
svlad2 [7]
69 out of 100  because if you turn 3/10 into a fraction with a like denominator as 39/100 you get 30/100 and then you add 39 and 30 and get 69/100

4 0
3 years ago
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