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
Afina-wow [57]
2 years ago
13

D%7D%7B5%C3%97%285%29%5E%7B2n%2B3%20%7D-%20%2825%29%5E%7Bn%2B1%E2%80%8B%7D%7D%20%5C%5C%20" id="TexFormula1" title="Simplify: \frac{ 5×(25)^{n+1} - 25 × (5)^{2n}}{5×(5)^{2n+3 }- (25)^{n+1​}} \\ " alt="Simplify: \frac{ 5×(25)^{n+1} - 25 × (5)^{2n}}{5×(5)^{2n+3 }- (25)^{n+1​}} \\ " align="absmiddle" class="latex-formula">
Need help please"....."​
Mathematics
1 answer:
Katen [24]2 years ago
4 0

\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }

can be rewritten as

\rm \:  =  \: \dfrac{5 \times  { {(5}^{2} )}^{n + 1}  -  {5}^{2}  \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {( {5}^{2} )}^{n + 1} }

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{  {( {x}^{m} )}^{n}  \: = \:   {x}^{mn}}}} \\

And

\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

So, using this identity, we

\rm \:  =  \: \dfrac{5 \times  {5}^{2n + 2}  - {5}^{2n + 2} }{{5}^{2n + 3 + 1}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

\rm \:  =  \: \dfrac{4}{25 - 1}

\rm \:  =  \: \dfrac{4}{24}

\rm \:  =  \: \dfrac{1}{6}

<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

You might be interested in
How many ten thousands in 420189
zaharov [31]
There are 20 ten thousands
5 0
3 years ago
Answer to 3,4,5,6,7,8,9,10,11,12 !!
sineoko [7]
3. i=129; j=112
4.k=90;l=116;m=64;n=86
5.o=13;p=78;q=91
6.a=120;b=60;c=140
Can't see #7
You did 8 I believe
9.v=39;w=59;x=121
10.y=59;z=93
11.a=42;b=48;c=132
12.a=60;b=50;c=80;d=100
8 0
3 years ago
Triangle YES has sides YE=32cm and YS=42cm. Angle Y has a measure of 78 degrees. What is the measure of side SE?
KonstantinChe [14]
What kind of a triangle is it?
8 0
3 years ago
A group of forest rangers work 5 days per week. It takes them 3 days to plant trees on 1/3 acre. What is the unit rate in acres
Talja [164]
I would say 5/9 acres a week
7 0
3 years ago
Write a formula for the given measure. Let P represent the perimeter in inches, and w
mario62 [17]
PERIMETER = 2 (LENGTH + WIDTH)
PERIMETER = 2 LENGTH + 2 WIDTH

Given: Length 5 inches

P = 2(5 in) + 2w
P = 10 in + 2w

Perimeter is dependent in both length and width. Changes in any length of width will automatically change perimeter.

For find width using the perimeter formula:

P = 10 + 2w
P - 10 = 2w
(P-10)/2 = w
P/2  - 5 = w

w = P/2  -  5

If the perimeter and length is given, you can use the derived formula to solve for width.

4 0
3 years ago
Other questions:
  • Please help me answer the questions in the picture
    10·1 answer
  • Subtract these sets of matrix
    15·1 answer
  • Find the real zeros of f(x); there are 4 zeros
    14·2 answers
  • The box plot shows the science test scores for Mrs. Everly's students. Describe the shape of the distribution.
    6·2 answers
  • find the volume of the composite figure ( also I'm not going to redo this question becuase, u should be able to zoom in) Ok, ple
    14·2 answers
  • 5x -4y = -23<br><br> -5x + 9y =8
    7·1 answer
  • Help please screenshot
    13·1 answer
  • Hope this makes you day
    7·1 answer
  • PLZZZ HELP<br><br>Order these numbers from least to greatest. ​
    10·2 answers
  • Find each difference. if you get stuck consider using a numberline
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!