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
I am Lyosha [343]
2 years ago
11

Solve the following and explain your steps. Leave your answer in base-exponent form. (3^-2*4^-5*5^0)^-3*(4^-4/3^3)*3^3 please st

ep by step!!!!
Mathematics
1 answer:
Naily [24]2 years ago
4 0

Answer:

\boxed{2^{\frac{802}{27}} \cdot 3^9}

Step-by-step explanation:

<u>I will try to give as many details as possible. </u>

First of all, I just would like to say:

\text{Use } \LaTeX !

Texting in Latex is much more clear and depending on the question, just writing down without it may be confusing or ambiguous. Be together with Latex! (*^U^)人(≧V≦*)/

$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$

Note that

\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

\left(\dfrac{1}{3^2}  \cdot \dfrac{1}{4^5}  \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3

Also,

\boxed{a^{0} = 1, a\neq 0 }

\left(\dfrac{1}{9}  \cdot \dfrac{1}{1024}  \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27

Note

\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq  0}

\left(\dfrac{1}{9216}   \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27

\left(\dfrac{1}{9216}   \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)

\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)

\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)

Note

\boxed{\dfrac{1}{\dfrac{1}{a} }  = a}

9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)

\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)

Once

9216=2^{10}\cdot 3^2 \implies  9216^3=2^{30}\cdot 3^6

\boxed{(a \cdot b)^n=a^n \cdot b^n}

And

$4^{\frac{4}{27}} = 2^{\frac{8}{27} $

We have

\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)

Also, once

\boxed{\dfrac{c^a}{c^b}=c^{a-b}}

2^{30-\frac{8}{27}} \cdot 3^6\cdot 27

As

30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27}  =\dfrac{802}{27}

2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3

2^{\frac{802}{27}} \cdot 3^9

You might be interested in
Idk how to do this equation
AveGali [126]
The answer to your question is car A because every 1 gallon o gas it goes  33 MPH, car A also uses the least amount of gas. Hope this helps! ;D
7 0
3 years ago
6th grade math ! C: help please
densk [106]

Answer:

9

Step-by-step explanation:

45 Cookies... 5hrs

? cookies... 1 hr

45 ÷ 5 = 9

9 cookies per hour

7 0
2 years ago
What is -3+5+6g=11-3g solve for g
vitfil [10]

Answer: g = 1

Step-by-step explanation:

-3 + 5 + 6g = 11 - 3g

First, we need to combine like terms

-3 + 5 = 2

2 + 6g = 11 - 3g

Add 3g to each side

2 + 9g = 11

Subtract 2 from each side

9g = 9

Divide each side by 1

g = 1

8 0
2 years ago
Read 2 more answers
Evaluate the expression: -0.75 - (-1 7/8)
m_a_m_a [10]

Answer:

9/8

Decimal form: 1.25

Mixed Number form: 1 1/8

Good luck, hope this helped!

4 0
2 years ago
Complete the table for the given rule. Rule: y = x/2 - 1<br><br> X Y<br> 4 =<br> 6 =<br> 8 =
Veseljchak [2.6K]

\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} 4&\stackrel{\frac{4}{2}-1}{1}\\&\\ 6&\stackrel{\frac{6}{2}-1}{2}\\&\\ 8&\stackrel{\frac{8}{2}-1}{3}\\ &\\ \cline{1-2} \end{array}

5 0
3 years ago
Other questions:
  • Please help me! See attached file on the side or up top where ever it is
    9·2 answers
  • I can’t find the answer please help
    15·2 answers
  • 2^2 + (2√3)^2 = y^2<br><br> Please help!
    5·1 answer
  • I need help with this question
    6·1 answer
  • there are 640 students in one school. How many boys are there if it is known that 1/4 of the number of girls is equal to one six
    5·2 answers
  • Which equation shows how to rewrite the sum of 30 and 45 using their greatest common factor? 30 + 45 = 5(6 + 9) 30 + 45 = 15(2 +
    5·1 answer
  • FR.EE POI.NTS!!!!!!!! I HOPE U HAVE/HAD A NICE DAY OR NIGHT
    9·1 answer
  • I need this for math thanks
    10·2 answers
  • How would you describe the shape of the distribution of the data? How is it skewed?
    7·1 answer
  • Lee is traveling by train to visit his grandmother. After 1 hour, he has 270 miles left to travel. After 2 hours, he has 180 mil
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!