Question

How do you rewrite \[{140^{\dfrac{1}{8}}}\] in radical form?

Answer 1

Hint:The given number is in the form exponent, where the exponent number is the number of times is multiplied by itself. The power term of the given number is in the form of fraction. The number should be written in the form radical that is in the form of roots.

Complete step by step explanation:Here in this question the number is in the form of exponent and we have to convert it into the radical form. The radical form is that it includes the roots like square root, cube roots or any roots. The radical form if it is a simplified radical it should satisfy the radicand must be less than index. No radicals appear in the denominator of a fraction.
The radical form is in the form of surds since the radical form includes the root symbols
The general form of exponent is \[{b^{\dfrac{1}{n}}}\] where n is called index and the b is the
radicand. The general form of radical is \[\sqrt[n]{b}\]

Now consider the given number \[{140^{\dfrac{1}{8}}}\] . Here the index is 8 and the radicand is 140. The radical form for the number \[{140^{\dfrac{1}{8}}}\] is written as \[\sqrt[8]{{140}}\] .

This is not a simplified radical form because the radicand is not less than index.

Therefore, the radical form of number \[{140^{\dfrac{1}{8}}}\] is \[\sqrt[8]{{140}}\]

Note:If a number is multiplied by itself by the number of times that number can be written in the form exponent. If the exponent is in the form of fraction it can be written in the form of roots. The radical form is the form of surd. Since surds also include the roots terms.