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
ioda
3 years ago
10

What is the following product? Assume x ≥ 0

Mathematics
1 answer:
Savatey [412]3 years ago
4 0

For this case we must multiply the following expression:

\sqrt [3] {x ^ 2} * \sqrt [4] {x ^ 3}

By definition of properties of otencias and roots we have:

\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

We rewrite the terms of the expression:

\sqrt [3] {x ^ 2} = (x ^ 2) ^ {\frac {1} {3}} = (x ^ 2) ^ {\frac {4} {12}}\\\sqrt [4] {x ^ 3} = (x ^ 3) ^ {\frac {1} {4}} = (x ^ 3) ^ {\frac {3} {12}}

So, we have:

(x ^ 2) ^ {\frac {4} {12}} * (x ^ 3) ^ {\frac {3} {12}} =

Applying the above definition we have:

\sqrt [12] {(x ^ 2) ^ 4} * \sqrt [12] {(x ^ 3) ^ 3} =

We multiply the exponents:

\sqrt [12] {x ^ 8} * \sqrt [12] {x ^ 9} =

We combine using the product rule for radicals.

\sqrt [12] {x ^ 8 * x ^ 9} =

By definition of multiplication properties of powers of the same base, we put the same base and add the exponents:

\sqrt [12] {x ^ {8 + 9}} =\\\sqrt [12] {x ^ {17}} =\\\sqrt [12] {x ^ {12} * x ^ 5} =\\x \sqrt [12] {x ^ 5}

Answer:

Option C

You might be interested in
James has 36 tulips. He must put the same number of tulips in each vase. How many tulips could be in each vase
k0ka [10]
1,2,3,4,6,9,12,18,36



please can i have a brainliest

7 0
4 years ago
Read 2 more answers
Dottie has 1400 U.S. dollars. If 1 New Zealand dollar equals 0.7059 U.S. dollars, about how many New Zealand dollars can Dottie
Andrew [12]
D. $988.26

1400 x 0.7059 = 988.26
5 0
3 years ago
Read 2 more answers
Solve.<br>4a + 3b + c = 3<br>a-3b + 2c = 4<br>11a-2b +3c = -1<br>​
rusak2 [61]

Answer:

-60

Step-by-step explanation:

4a+3b+c=-3;a-3b+2c=-23;11a-2b+3c=-60

8 0
4 years ago
What is 50/20 fully reduced?
horsena [70]
2 1/2 because 50-20 leaves you with 30 so you have one. Than 30-20 leaves you with 10. Now you have two. There isn't another 20 but 10 is half of twenty so that gives you a half so it is 2 1/2
6 0
3 years ago
Read 2 more answers
What is the LCD of these fractions?<br><br><br>5/x + 5/x+y
kirza4 [7]

the answer should be: x^2+xy

8 0
3 years ago
Other questions:
  • Can someone tell me how to do this! #2 &amp; #4
    14·2 answers
  • Find an equation of the line that passes through the points (- 4, 3) and (4, - 3) both slope-intercept form and standard form
    14·1 answer
  • Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side?
    8·1 answer
  • For the following question, what is the value of x to the nearest tenth?
    11·2 answers
  • How many solutions does the system of equations have? 2x + 3y = 6 y=-2/3x-1A. 0 B. 1 C. 2 D. infinite
    8·2 answers
  • Please help ? Question 27 and question 28
    12·1 answer
  • There are two numbers which sum to 16. If one number is eight less than three times the other, find the numbers.
    9·1 answer
  • Which ordered pair is the solution to the system of equations below when using the matrix tool?
    14·1 answer
  • Determine the change to the base of a triangle if the height is tripled and the area is 12 times larger than the original.
    10·1 answer
  • If you roll 2 dice, what is the probability of rolling a total of 3?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!