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
dimulka [17.4K]
3 years ago
10

Simplify ( 8∙4∙2 8∙7 )^2 × ( 8 0 7−3 )^3 × 7 −9 .

Mathematics
1 answer:
stich3 [128]3 years ago
4 0

\bf ~\hspace{7em}\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
~\hspace{4.5em}
a^n\implies \cfrac{1}{a^{-n}}
~\hspace{4.5em}
\cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\left( \cfrac{8\cdot 4\cdot 2}{8\cdot 7} \right)^2\times \left( \cfrac{8^0}{7^{-3}} \right)^3\times 7^{-9}\implies \left( \cfrac{8\cdot 8}{8\cdot 7} \right)^2\times \left( \cfrac{1\cdot 7^3}{1} \right)^3\times \cfrac{1}{7^9}


\bf \left( \cfrac{8}{8}\cdot \cfrac{8}{7} \right)^2\times (7^3)^3\times \cfrac{1}{7^9}\implies \left( \cfrac{8}{7} \right)^2\times 7^{3\cdot 3}\times \cfrac{1}{7^9}\implies \cfrac{8^2}{7^2}\times \cfrac{7^9}{7^9}
\\\\\\
\cfrac{8^2}{7^2}\implies \cfrac{64}{49}

You might be interested in
Write 45/72 in the simplest form
Oliga [24]
Hi! 

In my opinion, the easiest way to solve a problem like this is to find the greatest common factor (GCF) of the numerator and denominator and then divide both numbers by the GCF. 

So first we need to find the factors of 45 and 72 and find the factor that has the most value that the two numbers both have. 

45: 1, 3, 5, 9, 15, and 45

72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

It looks like the GCF is 9. Now we have to divide 45 and 72 by 9. 

45 ÷ 9 = 5

72 ÷ 9 = 8

So the correct answer should be:

\frac{45}{72} =  \frac{5}{8}

Hope this helps :)
3 0
3 years ago
The teacher never taught this please help it’s for a grade
34kurt

Answer: D 2/3

Step-by-step explanation:

8 0
3 years ago
Don't know this please help
nikitadnepr [17]
I would say answer number 2
6 0
2 years ago
. Two bicyclists, Sarah and Emily, depart from the same location. Sarah heads N55°E at an average speed of 6 km/hr. Emily heads
Liula [17]

Answer:

The distance between them after 30 minutes is 6.5 km.

Step-by-step explanation:

Speed = \frac{distance}{time}

Sarah's speed = 6 km/hr = 1.6667 m/s

Emily's speed = 10 km/hr = 2.7778 m/s

The measure of angle between their bearings = 105^{o}

After 30 minutes (1800 seconds);

distance = speed x time

Sarah would have covered a distance = 1.6667 x 1800

                               = 3000 m

                               = 3 km

Emily would have covered a distance = 2.7778 x 1800

                               = 5000 m

                               = 5 km

The distance between them, a, can be determined by applying the cosine rule;

a^{2} = b^{2} + c^{2} - 2bcCos A

   = 5000^{2} + 3000^{2} -2(5000 x 3000) Cos 105

   = 5000^{2} + 3000^{2} -2(5000 x 3000) x (-0.2588)

   = 2.5 x 10^{7} + 9 x 10^{6} + 7764000

   = 41764000

a = \sqrt{41764000}

  = 6462.5073

a = 6462.5 m

The distance between them after 30 minutes is 6.5 km.

4 0
2 years ago
What expression is equavalent to -72x+60
lozanna [386]
-36x+30

-24x+20

-18x+15

-12x+10


8 0
3 years ago
Other questions:
  • The average man takes 7192 steps a day about how many steps does the average man take in a year
    10·1 answer
  • Please answer correctly, will mark brainliest
    5·1 answer
  • I need help pleaseeeeee
    10·1 answer
  • EJ has shown that a function, f(x) grows by 12% for every unit in the domain. What does this prove?
    7·2 answers
  • Read each relationship and decide whether its graph would be continuous or discrete
    11·1 answer
  • Dawn, the teller, counted
    9·1 answer
  • Pls help pls pls hii lol bye hahaha math fractions lol. videostar
    7·1 answer
  • P(x)=2x^3-11x^2+ax-40 if x+4 is a factor of this polynomial what is the value of a
    14·1 answer
  • PLS HELP WITH THIS ILL GIVE BRAINLIST
    6·2 answers
  • A ride ticket usually costs
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!