# Math Help - Radical Multiplication

See attachment for math question.
I have to multiply and then simplify.

2. Originally Posted by sologuitar
See attachment for math question.
I have to multiply and then simplify.
$\sqrt{2^{109}} \cdot \sqrt{x^{306}} \cdot \sqrt{x^{11}} = 2^{\frac{109}2} \cdot x^{\frac{306}2} \cdot x^{\frac{11}2}$

Use the law of powers:

$a^x \cdot a^y = a^{x+y}$

Btw: $2^{\frac{109}2} = 2^{54+\frac12}$

3. ## I got...

Originally Posted by earboth
$\sqrt{2^{109}} \cdot \sqrt{x^{306}} \cdot \sqrt{x^{11}} = 2^{\frac{109}2} \cdot x^{\frac{306}2} \cdot x^{\frac{11}2}$

Use the law of powers:

$a^x \cdot a^y = a^{x+y}$

Btw: $2^{\frac{109}2} = 2^{54+\frac12}$
I got [2^(109/2)] [(x^(317/2)]

Base 2 and base x are not the same and so, we cannot apply the rule
a^x * a^y.

Correct?