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
What is -x^2+14+7x^5 in standard form
sasho [114]

Answer:

7x^5-x^2+14

Step-by-step explanation:

Hope this is what you are looking for!

5 0
3 years ago
UNICORN A IS 15 TIMES OLDER THAN
shtirl [24]

Answer:

Unicorn A is 300 years old

Unicorn B is 20 years old

Explanation:

15x + x = 320

16x = 320

x = 20

15 * 20 + 20 = 320

5 0
3 years ago
Read 2 more answers
What is the value of x which proves that the runways are parallel? What is the measure of the larger angle?
Semenov [28]

The answer is<u> C) x = 25; 107 degrees </u>

6 0
3 years ago
Read 2 more answers
The revised Daily Value for calcium is 1,300 mg per day. How many servings of this food would you have to eat to get 100% DV for
Ne4ueva [31]

Answer:

Taking into account the values showed for this food (image attached). It is required

5  

Servings.  

Step-by-step explanation:

The total calcium (Cat) required is 1300 mg/day.  

One serving of this food can have 260 mg.  

First step is to suppose one day of calculation. t = 1 day.

Cat = (1300 mg/day)(1 day) = 1300 mg Calcium.

One single serving can have 260 mg Calcium (Cas). So, we need to calculate the amount of servings (N) required to complete 1300 mg.

Cat = Cas*N

N = Cat/Cas = 1300 mg/260mg

N = 5.

Finally amount of servings is five N = 5.  

8 0
3 years ago
Solve for x <br> x-31=-90<br><br> show how you got the answer
Vinil7 [7]

Answer:

x= -59

Step-by-step explanation:

x-31=-90

Adding 31 to both sides we get

x-31+31=-90+31

x=-59

4 0
3 years ago
Read 2 more answers
Other questions:
  • A: 10x − 4y = 20 B: 8x + 6y = 14 Solve this system of equations using addition. Show all of your work. Also list the property th
    7·1 answer
  • Some one please help !!! How do I solve -1&lt;-x/3&lt;1
    8·1 answer
  • Please answer only if you know for sure :) Comes from pre-calc btw
    7·2 answers
  • Identify the domain of the function shown in the graph,
    14·1 answer
  • How do you graph the linear function g(x)=−4+7x
    10·2 answers
  • Which steps should be used to graph the equation y-<br> - 1x + 2)?
    15·1 answer
  • Cam borrows $1,00 from her bank. She will pay back the loan at a simple annual interest rate of 4% over 4 years. How much will s
    13·1 answer
  • HELP MEEMEMEMEMEMEMEMEMEMEMEMEMEMEMEME
    9·2 answers
  • Answer asap thank you?!!!!!<br> 1.
    5·2 answers
  • Riley is also making boxes to hold baseballs. She wants the dimensions of her boxes
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!