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Delvig [45]
1 year ago
14

Simplify the expression. Rewrite using only positive exponents.

Mathematics
1 answer:
Dvinal [7]1 year ago
4 0

The simplified form of the given expression is x^{18}a^{3}b^{3}.

The given expression is (\frac{x^{4}a^{2}b^{3} }{x^{-2}ab^{2}} )^{3}.

We need to simplify the given expression.

<h3>What are the basic laws of exponents?</h3>

The basic laws of exponents are as follows:

a^{m} \times b^{m} =(ab)^{m}

a^{m} \div b^{m} =(\frac{a}{b} )^{m}

a^{m} \times a^{n} =(a)^{m+n}

a^{m} \div a^{n} =(a)^{m-n}

Now, (\frac{x^{6}a^{2}b^{3} }{ab^{2}} )^{3}=(\frac{x^{18}a^{6}b^{9} }{a^{3}b^{6}} )

=x^{18}a^{3}b^{3}

Therefore, the simplified form of the given expression is x^{18}a^{3}b^{3}.

To learn more about the exponents visit:

brainly.com/question/26296886.

#SPJ1

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This is the answer on my test. this is correct.

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The first three terms of an arithmetic progression are m,12 and n . Find the value of m+n​
Vera_Pavlovna [14]
<h3>Answer:  24</h3>

===========================================

Explanation:

There are a few approaches. Here's one way to solve.

Let d be the common difference between the terms.

We add d to each term of this arithmetic sequence to get the next term.

  • First term = m
  • Second term = 12 = m+d
  • Third term = n = (m+d)+d = m+2d

Focusing on the second equation, we can solve for d like so

m+d = 12

d = 12-m

This is then plugged into the third equation

n = m+2d

n = m+2(12-m)

n = m+24-2m

n = 24-m

Therefore,

m+n = m+(24-m) = 24

It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.

-----------------

A more concrete example:

Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.

Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.

If d = 10, then the third term must be n = 12+d = 12+10 = 22

We can then see that m+n = 2+22 = 24

-----------------

I'll do another example:

m = 5

d = 12-m = 12-5 = 7

n = 12+d = 7 = 19

m+n = 5+19 = 24

Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.

-----------------

An alternative way to get the answer:

Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.

The midpoint of m and n is (m+n)/2

Set this equal to 12 and isolate the "m+n"

(firstTerm+thirdTerm)/2 = second term

(m+n)/2 = 12

m+n = 2*12

m+n = 24

So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.

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The quotient = 4x - 17 and the remainder = 54

Step-by-step explanation:

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hjlf

Answer:

20

Step-by-step explanation:

According to the question,five over 25 divided by 100

Can also be written as

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