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
Mila [183]
3 years ago
12

Wat is the simplified expression for 3^-4 • 2^3 • 3^2 over 2^4 • 3^-3

Mathematics
2 answers:
Irina18 [472]3 years ago
6 0
 (3^-4)(2^3)(3^2)  
----------------- 
(2^4)(3^-3)
I will keep this as simple as possible (for clarity). Any negative exponents should be switched from top to bottom and the negative sign removed from the exponent. 

(3^3)(2^3)(3^2)  
----------------- 
(2^4)(3^4)

Add the like terms in the numerator

(3^5)(2^3)  
---------- 
(2^4)(3^4)

Since we have powers of 3 and powers of 2 in the numerator and denominator we can add them together (just like when we reduce other fractions)  For example, x^4/x => x^3, or x^1/x^6 => 1/x^5

3/2

Final answer 3/2. 
Ratling [72]3 years ago
3 0
The answer is:  "\frac{3}{2}" . 
______________________________________________ 
          (or, write as: "1<span>½" ; or,  "1.5").</span>
______________________________________________
Explanation:
______________________________________________
We are asked to simplify the given expression:
______________________________________________
  →  \frac{3^{-4}×2^{3}×3^{2} }{2^{4}×3^{-3}} &#10;&#10;  ;
______________________________________________
Note:  In the "numerator" :
_________________________
   →  2³  =  2 × 2 × 2  =  8 .

   →  3²  =  3 × 3  =  9 .
_________________________
Note:  In the "denominator" :
_________________________
   →  2⁴  =  2 × 2 × 2 × 2 = 16 .
_____________________________
     So, rewrite our expression; substituting "8" for "(2³)";
and substituting "9" for "(3²)" — [in the numerator] ;
and substituting:  "16" for "(2⁴)" — [in the denominator] ;
_____________________________________________________
   → AS FOLLOWS:
_____________________________________________________
   →  \frac{3^{-4}×2^{3}×3^{2} }{2^{4}×3^{-3}}  ;

          =  \frac{3^{-4}×8×(9}{16×3^{-3}} ;
_____________________________________________________
   →  Since we have an "8" in the "numerator"; and a "16" in the "denominator" —respectively;  and since both values, taken individually in the numerator—and taken individually in the denominator— are multiplied by other values as isolated numbers;  we can "cancel out" the "8" in the "numerator" to a "1"; and change the "16" in the "denominator" to a "2" ;  since:
            "16÷8 = 2" ; and since "8÷8=1" ;  that is: "8/16 = 1/2".  We can then "eliminate" the "1" in the "numerator";  since in the numerator, there are other values that are multiplied by this "1" ;  & any value multiplied by "1" is equal to that same value.
___________________________________________
So we can rewrite the expression, as follows:
___________________________________________
   →  \frac{3^{-4}×(9)}{2×3^{-3}} ;  

↔ Rearrange and rewrite as follows:
_______________________________________
     →   \frac{3^{-4}×(9)}{2×3^{-3}} 

    =  \frac{(9) *{3^{-4}}{2×3^{-3}} ;
____________________________________
   → Note the following properties of exponents:
__________________________________________
         ⇒  (\frac{a} {b} ⁿ  = \frac{ a^{n}}{b^{n}}   ;  
                      → (b ≠ 0) ; 
__________________________________________
         ⇒  (a^{m} )ⁿ =  aa^{(m*n)}};
__________________________________________
         ⇒  a^{m}  a^{n} =  a^{(m+n)};
<u><em>
and especially</em></u>:

         ⇒\frac{ a^{m}}{ a^{n}}  =  a^{(m-n)}   ;  (a  \neq  0) ;;

<u><em>and especially</em></u>:

         ⇒  a^{-n}  =  \frac{1}{(a^{n) }} ;  (a \neq  0););                       If "n" is a positive integer; and if "a" is a non-zero real number. 
   _____________________________________________________
         →  So;  (3⁻⁴) / (3⁻³)  = 3⁽⁽⁻⁴ ⁻ ⁽⁻³⁾⁾ = 3⁽⁻⁴ ⁺ ³⁾ = 3⁻¹  
                                         = \frac{1}{(3^{1})} =  \frac{1}{3} ; ;  
_______________________________________________________
         →  Rewrite the expression:
_________________________________________
         →  \frac{(9) *{3^{-4}}{2×3^{-3}} ; 
 
               =  \frac{(9*1)}{(2*3)} ;                =   \frac{9}{6} ;                = \frac{(9/3) }{(6/3)} ;                = \frac{3}{2} ; or; write as: " 1 ½ " ; or, write as: " 1.5 ".
_______________________________________________________
You might be interested in
PLEASE HELP FAST!! ILL MARK AS BRAINLIEST!! Graphing is the best choice when solving for the following system:
Sedaia [141]
False. You can find the solution more quickly by solving the system algebraically.

-4x + 2y = 18

Since y=-3x+4,
-4x + 2(-3x+4) = 18
-4x - 6x + 8 = 18
-10x = 10
x = -1
y = -3x+4 = 7
8 0
3 years ago
This shape is made using three semicircles The smaller semicircle have diameters of 10cm Calculate the shaded area Take 3.142 an
AleksandrR [38]

Answer:

The shaded area is 314.2 cm²

Step-by-step explanation:

Here we note that the shape consists of two small circles and one larger circle

The diameter of the larger semicircle is subtended by the two smaller semicircles, the small semicircle closer to the left of the internal circumference of the larger semicircle is shaded one while the one on the right is without color,

Therefore,

Diameter of larger semicircle = 2 × 10 = 20 cm

Based on the diagram, the shaded area is observed to be;

Shaded area = Area of semicircle formed by larger diameter or 20 cm + Area area formed by the small semicircle close to the right of the internal circumference of the larger semicircle - Area area formed by the other smaller semicircle

Since the diameter and therefore the areas of the two small semicircles are equal, we have;

Shaded area = Area formed by the complete larger semicircle = Area of semicircle formed by larger diameter or 20 cm

∴ Shaded area = π·D²/4 = π×20²/4 = 100×3.142 cm² = 314.2 cm².

6 0
3 years ago
If cos θ &gt; 0 and tan θ &gt; 0, which of the following statements MUST be true? (5 points)
solniwko [45]

Yo sup??

cosx>0 in the 1st and 4th quadrant.

tanx>0 in the 1st and 3rd quadrant.

therefore the common solution is x lies in 1st quadrant.

Hence the correct answer is option A.

Hope this helps

5 0
3 years ago
40$ to the markup rate of 65% what is the final price?
djyliett [7]

Answer:

$66

Step-by-step explanation:

that's the answer I thinkkkk

4 0
3 years ago
Evaluate -3x+4y when x=-7 y=-10
Alexus [3.1K]

Answer:

-19

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • A car factory can build 14 cars in 4 hours. <br><br> How many cars can it build in 7 hours?
    13·1 answer
  • (4x^2-10x+6) divide (4x+2)
    6·1 answer
  • True or False? All equiangular triangles are similar.
    9·1 answer
  • An air conditioning system can circulate 400 cubic feet of air per minute. How many cubic yards of air can it circulate per minu
    14·1 answer
  • Which represents “4 more than one half a number”?
    8·2 answers
  • Write three hundred eighty-seven thousandths as a decimal number.<br>​
    9·2 answers
  • HELP 100 POINTS PLEASE GET IT RIGHT
    9·2 answers
  • If a driver drives at a constant rate of 38 miles per​ hour, how long would it take the driver to drive 247 miles?
    6·1 answer
  • (2 pts.) 9.) Find two equivalent expressions to tan 20° using the cotangent function in degrees.
    9·1 answer
  • Having issues with solving this
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!