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Colt1911 [192]
3 years ago
10

What is p^m ⋅ p^n equal to? p^m − n p^m + n p^m ⋅ n p^m ÷ n. please show work

Mathematics
1 answer:
Inessa05 [86]3 years ago
8 0
<h3>Answer:</h3>

p^(m+n) . . . . . . . parentheses are required

<h3>Explanation:</h3>

The answer follows directly from the rules of exponents:

... (a^b)×(a^c) = a^(b+c)

Here, you have a=p, b=m, c=n, so

... (p^m)×(p^n) = p^(m+n)

_____

<em>Where the rule comes from</em>

An exponent sigifies <em>repeated multiplication</em>. That is ...

... p^3 = p·p·p . . . . . . . the exponent means p is a factor 3 times

... p^2 = p·p . . . . . . . . .the exponent means p is a factor 2 times

When we multiply these terms together, we have ...

... (p^3)×(p^2) = (p·p·p)×(p·p) = p·p·p·p·p = p^(2+3) = p^5

The number of times p is a factor of the product is the total of the number of times p is a factor in the factors of the product.

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Sergio [31]

Answer:

310 pages in book = 100%

Step-by-step explanation:

5 0
3 years ago
A 10ft by 20ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216ft^
Dmitry [639]

check the picture below.


so, we know the dimensions of the pool, is a 20x10, so its area is simply 200 ft², and we know the walkway is 216 ft², so the whole thing, including pool and walkway is really 200 + 216 ft².


now, as you see in the picture, the dimensions for the combined area is 20+2x and 10+2x, since the walkway is "x" long, therefore,


\bf \stackrel{length}{(20+2x)}\stackrel{width}{(10+2x)}=200+216\implies \stackrel{FOIL}{4x^2+60x+200}=200+216 \\\\\\ 4x^2+60x=216\implies \stackrel{dividing~by~4}{x^2+15x=54} \\\\\\ x^2+15x-54=0\implies (x+18)(x-3)=0\implies x= \begin{cases} -18\\ \boxed{3} \end{cases}


notice, it cannot be -18, since is a positive length unit.

5 0
3 years ago
Read 2 more answers
If I have a 68.70 in the grade book and I get a 56/100 on a test that’s worth 20% of my grade what will my grade be now?
Marizza181 [45]
U got a 44 on your test so 20 percent of 68.70 plus the 44
5 0
3 years ago
Read 2 more answers
Find the range and the interquartile range of the given data set.<br> 2, 4, 7, 8, 16, 19, 21
sashaice [31]
The range for the data given is 11
4 0
3 years ago
50 POINTS AND BRAINIEST PLEASE HELP
exis [7]

Answer:

<h2><u>y = -2x</u></h2>

Step-by-step explanation:

If you notice very carefully then you will see that the line passes through the points :

( 1 , - 2 )

( - 1 , 2 )

Hence the value of x = 1 when the value of y = - 2 .

We know that - 2 × 1 = - 2

⇒ - 2 x = y

⇒ y = - 2x

Hence the first OPTION is correct .

Verification :

For points ( - 1 , 2 ) we can write :

y = - 2x

⇒ 2 = - 2 × - 1

⇒ 2 = 2

Hence the answer is verified .

Always try to use the converse of the graphical method .

( Nothing converse is there ... just saying the opposite steps of that method :P )

I mean in graphical method we plot points and then join , here identify the joined points and then make the equation .

5 0
3 years ago
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