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
german
3 years ago
12

What is the simplified expression for,

Mathematics
1 answer:
Nostrana [21]3 years ago
6 0

Here are a few rules you need to know for this equation:

  • Multiplying exponents of the same base: x^m\times x^n=x^{m+n}
  • Dividing exponents of the same base: \frac{x^m}{x^n}=x^{m-n}
  • Turning a negative exponent to a positive one: x^{-m}=\frac{1}{x^m};\frac{1}{x^{-m}}=x^m

So this is our algebraic expression: \frac{3^{-4}\times 2^3\times 3^2}{2^4\times 3^{-3}}

Firstly, multiply 3^-4 and 3^2: \frac{3^{-4+2}\times 2^3}{2^4\times 3^{-3}}=\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}

Next, divide:

\frac{3^{-2}\times 2^3}{2^4\times 3^{-3}}=3^{-2-(-3)}2^{3-4}=3^12^{-1}

Next, turn the negative exponent into a positive one: 3^12^{-1}= \frac{3}{2}

<u>Your final answer is 3/2, or 1.5.</u>

You might be interested in
Please i need an answer urgently. Sum of 3 terms are 252, first term is 192. Find common ratio
Viefleur [7K]

Answer:

r=\frac{1}{4}\\\\r=-\frac{5}{4}

Step-by-step explanation:

<u>Geometric Sequences</u>

The geometric sequence is given as:

a_1, a_1r, a_1r^2, a_1r^3,..., a_1r^{n-1}

Where n is the number of the term, n≥1, and r is the common ratio.

The sum of n terms of the geometric sequence is given by:

\displaystyle S_n=a_1\frac{r^n-1}{r-1}

We are given: S3=252, a1=192, thus substuting:

\displaystyle 252=192\frac{r^3-1}{r-1}

Dividing by 12:

\displaystyle 21=16\frac{r^3-1}{r-1}

Recall that:

r^3-1=(r-1)(r^2+r+1)

Substituting:

\displaystyle 21=16\frac{(r-1)(r^2+r+1)}{r-1}

Simplifying:

21=16(r^2+r+1)=16r^2+16r+16

Rearranging:

16r^2+16r+16-21=0

16r^2+16r-5=0

Rewriting:

16r^2-4r+20r-5=0

Factoring:

4r(4r-1)+5(4r-1)=0

(4r-1)(4r+5)=0

Solving:

r=\frac{1}{4}\\\\r=-\frac{5}{4}

Both solutions are valid

6 0
3 years ago
What are the dimensions of a rectangle with an area of 18 square inches and a perimeter of 18 inches? A) 9 in. x 2 in.B) 5 in. x
Alina [70]

Answer:

C

Step-by-step explanation:

Area: 6 \times 3 = 18

Perimeter: 2 \times (6  + 3) = 18

4 0
2 years ago
Read 2 more answers
What is the volume of a container measured in liquid units
saveliy_v [14]

Step-by-step explanation:

liters

The capacity of a container is the volume of a container measured in liquid units. Cups, pints, quarts, and gallons are customary units of measurement. Two metric units of capacity are milliliters and liters. A milliliter is equal to about 20 drops from an eyedropper.

3 0
3 years ago
Read 2 more answers
ASAP!!!!!!!!!!!!!!!!!!!
steposvetlana [31]

Answer:

V = 2143.57 cm^3

Step-by-step explanation:

We want to find the volume of the sphere

V = 4/3 pi r^3 where r is the radius and pi = 3.14

V = 4/3 ( 3.14) ( 8)^3

V = 2143.57333 cm^3

Rounding to the nearest hundredth

V = 2143.57 cm^3

3 0
2 years ago
Read 2 more answers
If a barrel averages 50 pounds and a crate 160 ​pounds, write an inequality that describes when x barrels and y crates will caus
irakobra [83]

Answer:

https://iepa.org.au/network-news/it

Step-by-step explanation:

that link is answer

6 0
3 years ago
Other questions:
  • Suppose that circles A and B have a central angle measuring 100°. Additionally, the measure of the sector for circle A is 10π m2
    14·2 answers
  • A middle School English teacher polled random students about how many pages of a book they read per week. A= Janine says experim
    6·1 answer
  • Prove that when x is greater than one a triangle with side lengths a equals x squared minus one and c equals x squared plus one
    7·1 answer
  • Rewrite the equation y - 8 = 2(x + 4) into slop-intercept form
    6·1 answer
  • 5 points
    14·2 answers
  • Will give BRAINLIEST for the first correct answer with their steps!
    14·1 answer
  • Round 1.82 to the nearest whole number​
    10·2 answers
  • $<br> 20,524,945,000,000 rounded to the nearest billion
    10·1 answer
  • Decide where the first digit of the quotient should be placed. Do not complete the division. The first digit in the quotient of
    6·2 answers
  • The difference of three times a number and a second number is two. The sum of the two numbers is fourteen. What are the two numb
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!