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
Zina [86]
2 years ago
6

Which statement is true?​

Mathematics
1 answer:
love history [14]2 years ago
6 0
<h2>Hello!</h2>

The answer is:

The second option,

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

<h2>Why?</h2>

Discarding each given option in order to find the correct one, we have:

<h2>First option,</h2>

\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}

The statement is false, the correct form of the statement (according to the property of roots) is:

\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}

<h2>Second option,</h2>

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

The statement is true, we can prove it by using the following properties of exponents:

(a^{b})^{c}=a^{bc}

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

We are given the expression:

(\sqrt[m]{x^{a} } )^{b}

So, applying the properties, we have:

(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }

Hence,

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

<h2>Third option,</h2>

a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}

The statement is false, the correct form of the statement (according to the property of roots) is:

a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}

<h2>Fourth option,</h2>

\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}

The statement is false, the correct form of the statement (according to the property of roots) is:

\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }

Hence, the answer is, the statement that is true is the second statement:

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

Have a nice day!

You might be interested in
PLEASE ANSWER THIS QUESTION FOR 45 POINTS<br><br> How do you find the frequency of these numbers?
nignag [31]

Answer:

6 or 7

Step-by-step explanation:

3 0
2 years ago
The question is below
Tanzania [10]

Answer:

B. $4.75

Step-by-step explanation:

3(4) + 7 = 19

19/4=4.75

7 0
2 years ago
Read 2 more answers
Decide if the following scenario involves a permutation or combination. Then find the number of possibilities. The student body
Troyanec [42]

Answer:

735,130.

Step-by-step explanation:

The order of election of the 3 representatives does not matter so it is a combination.

The number of possible combinations

= 165! / 162! 3!

=  (165 * 164 * 163) / (3*2*1)

= 735,130.

6 0
3 years ago
Tell whether the statement is sometimes, always, or never true. Explain your reasoning. The x-coordinate of a point on the x-axi
Tom [10]
I think this would be sometimes true
3 0
3 years ago
Read 2 more answers
Solving systems of equations by substitution -2x-3(6-11)=-7
Papessa [141]

Answer:

11

Step-by-step explanation:

Simplify both sides of the equation.

Subtract 15 from both sides.

Divide both sides by -2.

x = 11

3 0
3 years ago
Other questions:
  • Solve . log (xy) where x=12 and y=20
    7·1 answer
  • Which graph represents the solution for the equation 4 3 x + 2 = 5x? A) A B) B C) C D) D
    6·2 answers
  • The science club raised money to clean the beach.They spent $29 on trash bags and $74 on waterproof boots.They still have $47 le
    10·1 answer
  • 20 CHILDREN WENT TO A CAFE FOR LUNCH.14 CHILDREN ATE FISH BURGERS. 10 CHILDREN ATE CHICKEN BURGERS. HOW MANY CHILDREN ATE BOTH F
    5·1 answer
  • The wheel of Theodorus 1 inch
    10·1 answer
  • Next question <br> lets keep going
    5·2 answers
  • Simplify -1(6 + 5)….
    14·2 answers
  • Please help me with this​
    5·1 answer
  • Nevaeh is a high school basketball player. How many points would Nevaeh score in a game if she made 2 free throws (worth one poi
    7·2 answers
  • How many US flags can a company make if they have 2500 stars
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!