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
Pavel [41]
3 years ago
12

Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

Mathematics
1 answer:
gtnhenbr [62]3 years ago
7 0

Answer:

Simplifying the expression (6^{-2})(3^{-3})(3*6)^4 we get \mathbf{108}

Step-by-step explanation:

We need to simplify the expression (6^{-2})(3^{-3})(3*6)^4

Solving:

(6^{-2})(3^{-3})(3*6)^4

Applying exponent rule: a^{-m}=\frac{1}{a^m}

=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\

Factors of 18=2\times 3\times 3=2\times3^2

Factors of 6=2\times 3

Replacing terms with factors

=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\

Using exponent rule: (a^m)^n=a^{m\times n}

=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}

Using exponent rule: a^m.a^n=a^{m+n}

=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}

Now using exponent rule: \frac{a^m}{a^n}=a^{m-n}

=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108

So, simplifying the expression (6^{-2})(3^{-3})(3*6)^4 we get \mathbf{108}

You might be interested in
A gardener has 27 pansies and 36 daisies.He plants an equal number of each type of flower in each row.What is the greatest possi
mojhsa [17]
I think it might be 3 rows. Hope this helped
6 0
3 years ago
Read 2 more answers
Is square meters a type of surface area
Irina18 [472]

Yes square meters is a type of surface area.

7 0
3 years ago
A customer pay 18 for a DVD that originally cost 20. What is the percent decrease in the cost of the DVD
natima [27]

The discount is $2. 2/20 is 0.1 or 1/10 which as a percentage would be 10%. The discount of $2 is <u><em>10%</em></u> off.

8 0
3 years ago
Can someone help only answer if you know no scam links or your getting reported.
skelet666 [1.2K]

Answer:

Volume= 10 cm³

Step-by-step explanation:

V=lwh

V=\frac{5}{4} *4*2

V=5*2

V=10

7 0
2 years ago
Read 2 more answers
Can anyone help. Got set this as homework and don’t understand anything
Vitek1552 [10]
That square in a means that it’s 90 degrees and b is 70. Well it says that ab = bc. And ab together is 90+70 which is 160. A straight line is 180 in total so to figure that other side of b out do 180-70 which is 110. So now you have 110, and to match ab you need 50 more degrees for bc. Therefore c is 50 degrees
5 0
2 years ago
Other questions:
  • Susie bought 3 pies all for the same price and a snickers bar for $1 Emma bought one of same pies and spent $9 on flowers, they
    14·1 answer
  • (5r+7)(5r-7)<br><br> *Multiplying Polynomials
    5·2 answers
  • Which test point holds true for 2/5x-1/5y≥0
    5·1 answer
  • Solve -3(2x - 9) = -3. <br> A. 5 <br> B. 4<br> C.-4<br> D.-5
    8·2 answers
  • Graph the function. Label the vertex and axis of symmetry. g(x)=4x^2-48x+7
    12·1 answer
  • Please help. I'll give brainliest :)
    7·1 answer
  • Enter the correct answer in the box.
    5·2 answers
  • What is the domain of the function<br> Y=2/x-5
    12·1 answer
  • Select the real-world problem that could be solved using a proportion.
    15·1 answer
  • Betty has the option of using three types of tables in her coffee shop:
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!