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spin [16.1K]
3 years ago
13

Express a^6n/a^3n with positive exponents

Mathematics
2 answers:
Nat2105 [25]3 years ago
7 0
I hope this helps you





a^6n-3n



a^3n
goldfiish [28.3K]3 years ago
4 0

Answer: Our required exponential form would be a^{6n-3n}=a^{3n}

Step-by-step explanation:

Since we have given that

\dfrac{a^{6n}}{a^{3n}}\\

We need to write in positive exponents:

According to law of exponents:

a^m\div a^n=a^{m-n}

So, using this, our expression becomes,

a^{6n-3n}=a^{3n}

Hence, our required exponential form would be a^{6n-3n}=a^{3n}

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Read 2 more answers
The perimeter of equilateral triangle ABC is 81/3 centimeters, find the length of the radius and apothem.
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There is a typo error, the perimeter of equilateral triangle ABC is 81/√3 centimeters.

Answer:

Radius = OB= 27 cm

Apothem = 13.5 cm

A diagram is attached for reference.

Step-by-step explanation:

Given,

The perimeter of equilateral triangle ABC is 81/√3 centimeters.

Substituting this in the formula of perimeter of equilateral triangle =3\times\ side

3\times\ side =[tex]81\sqrt{3}

Side = \frac{81\sqrt{3} }{3} =27\sqrt{3} \ cm

Thus from the diagram , Side AB=BC=AC= 27\sqrt{3} \ cm

We know each angle of an equilateral triangle is 60°.

From the diagram, OB is an angle bisector.

Thus \angle OBC = 30°

Apothem is the line segment from the mid point of any side to the center the equilateral triangle.

Therefore considering ΔOBE, and applying tan function.

tan\theta =\frac{perpendicular}{base} \\tan\theta=\frac{OE}{BE} \\tan\theta=\frac{OE}{\frac{27\sqrt{3}}{2}  } \\tan30\times {\frac{27\sqrt{3} }{2} }= OE\\\frac{1}{\sqrt{3} } \times\frac{27\sqrt{3} }{2} =OE\\

Thus ,apothem  OE= 13.5 cm

Now for radius,

We consider ΔOBE

cos\theta=\frac{base}{hypotenuse} \\cos30= \frac{BE}{OB} \\Cos30 = \frac{\frac{27\sqrt{3} }{2}}{OB}  \\OB= \frac{\frac{27\sqrt{3} }{2}}{cos30} \\OB= \frac{\frac{27\sqrt{3} }{2}}{\frac{\sqrt{3} }{2} } \\OB =27 \ cm

Thus for

Perimeter of equilateral triangle ABC is 81/√3 centimeters,

The radius of equilateral triangle ABC is 27 cm

The apothem of equilateral triangle ABC is 13.5 cm

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