Solve the following exercise:

$\sqrt{10}\cdot\sqrt{3}=$

To simplify the given expression, **we use two laws of exponents**:

__A.__ Defining the root as an exponent:

$\sqrt[n]{a}=a^{\frac{1}{n}}$__B.__ The law of exponents for dividing powers with the same base** (in the opposite direction)**:

$x^n\cdot y^n =(x\cdot y)^n$

__Let's start__ by using the law of exponents shown in **A**:

$\sqrt{10}\cdot\sqrt{3}= \\
\downarrow\\
10^{\frac{1}{2}}\cdot3^{\frac{1}{2}}=$We continue, __since we have a multiplication between two terms with ____equal exponents__, we can use the law of exponents shown in **B **__and combine them under the same base which is ____raised to the same exponent____:__

$10^{\frac{1}{2}}\cdot3^{\frac{1}{2}}= \\
(10\cdot3)^{\frac{1}{2}}=\\
30^{\frac{1}{2}}=\\
\boxed{\sqrt{30}}$In the last steps, we performed the multiplication of the bases and used the definition of the root as an exponent shown earlier in **A** __(in the opposite direction)__** **to return to the root notation.

__Therefore, the correct answer is B.__