Respuesta :
The simplified form of the expression is [tex]10 x^{18}[/tex].
What are indices in maths?
- An index, or a power, is the small floating number that goes next to a number or letter.
- The plural of index is indices. Indices show how many times a number or letter has been multiplied by itself.
The given expression is [tex]\sqrt{100x^{36} }[/tex]
Applying the rule, [tex]\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}[/tex]
Now, [tex]\sqrt{100} \sqrt{x^{36} }[/tex]
Simplifying, we get;
[tex]10\sqrt{x^{36} }[/tex]
Applying the exponent rule, [tex]a^{bc} = (a^{b} )^{c}[/tex]
We get
[tex]10 \sqrt{(x^{18} })^{2}[/tex]
[tex]10 x^{18}[/tex]
Therefore, the simplified form of the expression is [tex]10 x^{18}[/tex].
Learn more about indices
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