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]
3 years ago
6

Which statement is true?​

Mathematics
1 answer:
love history [14]3 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
<img src="https://tex.z-dn.net/?f=12x%20%5E%7B2%7D%20%20%2B%204x%20%2B%2020" id="TexFormula1" title="12x ^{2} + 4x + 20" alt="1
Nesterboy [21]
<h3>Answer: </h3>

The GCF is 4

The polynomial factors to 4(3x^2+x+5)

==========================================================

Further explanation:

Ignore the x terms

We're looking for the GCF of 12, 4 and 20

Factor each to their prime factorization. It might help to do a factor tree, but this is optional.

  • 12 = 2*2*3
  • 4 = 2*2
  • 20 = 2*2*5

Each factorization involves "2*2", which means 2*2 = 4 is the GCF here.

We can then factor like so

12x^2 + 4x + 20\\\\4*3x^2 + 4*x + 4*5\\\\4(3x^2 + x + 5)

The distributive property pulls out that common 4. We can verify this by distributing the 4 back in, so we get the original expression back again.

The polynomial inside the parenthesis cannot be factored further. Proof of this can be found by looking at the roots and noticing that they aren't rational numbers (use the quadratic formula).

4 0
2 years ago
Help please &gt;3 thank youuu
11111nata11111 [884]

Answer:

C

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the domain of the function below? (0,2 (3,1) (5,2) (8,4)
KiRa [710]
{0,3,5,8} ok  this0 is the an0sw0er
7 0
3 years ago
Read 2 more answers
Can someone please help and explain how to use the Pythagorean Theorem to prove a triangle is a right triangle.
marin [14]

Hi there!

For the Pythagorean Theorem, basically you just need to apply this formula: a^2 + b^2 = c^2

And then find the root of the hypotenuse.

For example,

15^2 + 8^2 = the hypotenuse^2

Which equals, 225 + 64 = 289

Square root of 289 = 17

Please mark me brainliest if this helps!

Have a wonderful day!

7 0
3 years ago
Has anyone done the segment one practice exam in geometry
konstantin123 [22]
I have done the segment 1 pratice exam
5 0
3 years ago
Other questions:
  • Please help this is my last try
    11·1 answer
  • Describe the error Sarah made when simplifying the expression shown. -5(x-2)=-5x-10
    9·1 answer
  • 14.8 ounces, 15.5 ounces, 14.6 ounces, and 15.4 ounces. Estimate the total weight of the four packages.
    11·2 answers
  • What are two solutions to x&gt;29
    6·1 answer
  • . What is the value of x? rectangle with length 45 feet, width x feet, and diagonal 53 feet
    15·1 answer
  • PLZ HELP ASAP <br><br> image above^❤️
    13·2 answers
  • There is a bag filled with 3 blue and 4 red marbles.
    7·1 answer
  • If u steal point i report
    7·1 answer
  • Consider the system and find the eigenvalues and the eigenvectors
    5·1 answer
  • Please solve this one
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!