Solve Square Root Multiplication: √7 × √7 Simplification

In order to simplify the given expression, we will use two laws of exponents:

a. The definition of root as an exponent:

$\sqrt[n]{a}=a^{\frac{1}{n}}$b. The law of exponents for power of a power:

$(a^m)^n=a^{m\cdot n}$

Let's start by converting the square roots to exponents using the law mentioned in a':

$\sqrt{7}\cdot\sqrt{7}= \\ \downarrow\\ 7^{\frac{1}{2}}\cdot7^{\frac{1}{2}}=$Let's continue, notice that we got a number multiplied by itself, therefore, according to the definition of exponents we can write the expression we got as a power of that same number, then - we'll use the law of exponents mentioned in b' and perform the exponentiation on the term in parentheses:

$7^{\frac{1}{2}}\cdot7^{\frac{1}{2}}= \\ (7^{\frac{1}{2}})^2=\\ 7^{\frac{1}{2}\cdot2}=\\ 7^1=\\ \boxed{7}$Therefore, the correct answer is answer a'.