Divide x to the 3 fourths power divided by x to the 1 sixth power.

Solution:

It is given that x to the 3 fourths power divided by x to the 1 sixth power

We can write it as

x^3/4 / x^1/6

By using the exponential property

xⁿ / x^m = x^{(n - m)}

We get

x^3/4 / x^1/6 = x^{(3/4 - 1/6)}

=x^7/12

Therefore, by dividing x to the 3 fourths power divided by x to the 1 sixth power we get x^7/12.

Example - Divide x to the 1 fourths power divided by x to the 1 fourth power.

Solution:

It is given that

x to the 1 fourths power divided by x to the 1 fourth power

We can write it as

x^1/4 / x^1/4

By using the exponential property

xⁿ / x^m = x^{(n - m)}

We get

x^1/4 / x^1/4 = x^{(1/4 - 1/4)}

= x⁰

= 1
Therefore, by dividing x to the 1 fourths power divided by x to the 1 fourth power we get 1.

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Divide x to the 3 fourths power divided by x to the 1 sixth power.

Summary:

Dividing x to the 3 fourths power divided by x to the 1 sixth power we get x^7/12.