Given:
The given expression is [tex]\sqrt{100 x^{36}}[/tex]
We need to determine the simplified form of the expression.
Simplified form of the expression:
Let us determine the simplified form of the expression.
Applying the rule, [tex]\sqrt[n]{a b}=\sqrt[n]{a} \sqrt[n]{b}[/tex]
We get;
[tex]\sqrt{100} \sqrt{x^{36}}[/tex]
Simplifying, we get;
[tex]10 \sqrt{x^{36}}[/tex]
Applying the exponent rule, [tex]a^{b c}=\left(a^{b}\right)^{c}[/tex], we have;
[tex]10 \sqrt{\left(x^{18}\right)^{2}}[/tex]
Simplifying, we get;
[tex]10 x^{18}[/tex]
Thus, the simplified form of the expression is [tex]10 x^{18}[/tex]
Hence, Option A is the correct answer.
