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
liraira [26]
2 years ago
10

(27/8)^1/3×[243/32)^1/5÷(2/3)^2]Simplify this question sir pleasehelpme​

Mathematics
2 answers:
gtnhenbr [62]2 years ago
6 0

Step-by-step explanation:

=  {( \frac{27}{8} )}^{ \frac{1}{3} }  \times ( \frac{243}{32} )^{ \frac{1}{5} }  \div  {( \frac{2}{3} )}^{2}

=  { ({ (\frac{3}{2} )}^{3}) }^{ \frac{1}{3} }  \times  {( {( \frac{3}{2}) }^{5} )}^{ \frac{1}{5} }  \div  {( \frac{2}{3} )}^{2}

=  {( \frac{3}{2} )}^{3 \times  \frac{1}{3} }  \times  {( \frac{3}{2} )}^{5 \times  \frac{1}{5} }  \times  {( \frac{3}{2} )}^{2}

=  \frac{3}{2}  \times  \frac{3}{2}  \times  {( \frac{3}{2} )}^{2}

=  {( \frac{3}{2} )}^{1 + 1 + 2}

=  {( \frac{3}{2} )}^{4} \:  or \:  \frac{81}{16}

Usimov [2.4K]2 years ago
3 0

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

\sf{\longmapsto{\bigg( \dfrac{27}{8} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{243}{32} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

We can write as :

27 = 3 × 3 × 3 = 3³

8 = 2 × 2 × 2 = 2³

243 = 3 × 3 × 3 × 3 × 3 = 3⁵

32 = 2 × 2 × 2 ×2 × 2 = 2⁵

\sf{\longmapsto{\bigg( \dfrac{3 \times 3 \times 3}{2 \times 2 \times 2} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{{(3)}^{3}}{{(2)}^{3}} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{({3}^{5})}{{(2)}^{5}} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

Now, we can write as :

(3³/2³) = (3/2)³

(3⁵/2⁵) = (3/2)⁵

\sf{\longmapsto{\left\{\bigg(\frac{3}{2} \bigg)^{3}  \right\}^{\frac{1}{3}} \times \Bigg[\left\{\bigg(\frac{3}{2} \bigg)^{5} \right\}^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

Now using law of exponent :

{\sf{({a}^{m})^{n} = {a}^{mn}}}

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{3 \times \frac{1}{3}} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{5 \times \frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{\frac{3}{3}} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{\frac{5}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times\Bigg[\bigg(\frac{3}{2}  \bigg)^{1} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{3}{2} \bigg)^{2}\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{3}{2} \times  \dfrac{3}{2} \bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{3 \times 3}{2 \times 2}\bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2}  \bigg)^{1} \times  \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)\times \Bigg[\bigg(\frac{3}{2}  \bigg)\times  \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \:  \: \dfrac{3}{2}   \times \dfrac{9}{4} \:  \: \Bigg]}}\\

\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \:  \: \dfrac{3 \times 9}{2 \times 4} \:  \: \Bigg]}} \\

\sf{\longmapsto{\bigg(\dfrac{3}{2} \bigg)\times \Bigg[ \:  \: \dfrac{27}{8} \:  \: \Bigg]}} \\

\sf{\longmapsto{\dfrac{3}{2} \times \dfrac{27}{8}}} \\

\sf{\longmapsto{\dfrac{3 \times 27}{2 \times 8}}} \\

\sf{\longmapsto{\dfrac{81}{16}}\: ≈ \:5.0625\:\red{Ans.}} \\

You might be interested in
Solve by completing the square x^2-6x-4=0
Vesna [10]

Answer:

x = 3 ± \sqrt{13}

Step-by-step explanation:

x² - 6x - 4 = 0 ( add 4 to both sides )

x² - 6x = 4

To complete the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 3)x + 9 = 4 + 9

(x - 3)² = 13 ( take square root of both sides )

x - 3 = ± \sqrt{13} ( add 3 to both sides )

x = 3 ± \sqrt{13}

6 0
2 years ago
Find f(x) and g(x) so that the function can be described as y = f(g(x)).<br><br> y = 4/x^2+9
dlinn [17]

I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,

One possible answer is f(x) = \frac{4}{x},  \ \ g(x) = x^2+9

Another possible answer is f(x) = \frac{4}{x+9}, \ \ g(x) = x^2

There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)

So in the first example above, we would have

f(x) = \frac{4}{x}\\\\f( g(x) ) = \frac{4}{g(x)}\\\\f( g(x) ) = \frac{4}{x^2+9}

In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.

Similar steps will happen with the second example as well (when g(x) = x^2)

4 0
3 years ago
What is the sum of the interior angles in this shape?
Dmitrij [34]

Answer:

720° :)

Step-by-step explanation:

You can find the total interior angle for any shape using the following (n being the number of sides):

S = ( n - 2 ) × 180 °

S = (6-2) * 180

S = 720

5 0
3 years ago
Read 2 more answers
Is Triangle ACE congruent with SPY? Explain your reasoning.
gavmur [86]
ACE IS THE CORRECT ANSWER
This is because
The triangle a c and e
7 0
3 years ago
A radio controlled car travels 27 km and 28.5 minutes what is the speed of the car​
olya-2409 [2.1K]

Answer:

56.842 km/hr

0.947 km / min

15.789 m/s

Step-by-step explanation:

speed = distance / time

let's assume your teacher wants it in km/ hr

28.5 minutes = ? hours

60 minutes = 1 hour

we can multiply both sides of 60 minutes = 1 hour by 28.5/60 to get 28.5 minutes = 28.5/60 hours

distance = 27 km

27 km / (28.5/60) hours = 56.842 km/hr

in km / minute

27 km / 28.5 minutes = 0.947 km / min

in meters/second:

1 minute = 60 seconds

28.5 minutes = ? seconds

we can multiply both sides of the first equation by 28.5 to get

28.5 minutes = 1710 seconds

27 km = ? meters

1 km = 1000 meters

we can multiply both sides of the second equation by 27 to get

27km = 27000 meters

27000 meters / 1710 seconds = 15.789 m/s

3 0
2 years ago
Other questions:
  • Please i need help fast <br> find the missing term<br> blank 180 30 5
    12·2 answers
  • Mr Hughes is competing in the Mr. Legs campaign to raise money for the coral shores high school scholarship fund. On the first d
    14·2 answers
  • Denise provides water for the runners at her schools 10K road race. She has a container that holds 678 ounces of water. How many
    9·2 answers
  • Suppose $200 is invested at the annual interest rate 6% compounded continuously what is the amount in the account after years ?
    14·1 answer
  • Which of the following would be the coefficient of the third term of a binomial to the seventh power?
    12·1 answer
  • What is the area of the triangle?
    11·2 answers
  • PLSSS HELP! what is the slope-intercept equation of the line???
    15·1 answer
  • If it costs $1.40 per square foot to install the garden, what is the cost for plan A? Plan B
    11·1 answer
  • Write an equation that represents the relationship between
    9·1 answer
  • Help me plssssss i don’t know how to do this
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!