To simplify the expression [tex]\(\frac{3^{10}}{3^4}\)[/tex], we need to use the appropriate exponent laws.
The law that applies here is the quotient of powers law. This law states that when you divide two expressions with the same base, you subtract the exponents. This can be written as:
[tex]\[
\frac{a^m}{a^n} = a^{m-n}
\][/tex]
In the given expression [tex]\(\frac{3^{10}}{3^4}\)[/tex], the base [tex]\(a\)[/tex] is [tex]\(3\)[/tex], the exponent [tex]\(m\)[/tex] is [tex]\(10\)[/tex], and the exponent [tex]\(n\)[/tex] is [tex]\(4\)[/tex]. Applying the quotient of powers law:
[tex]\[
\frac{3^{10}}{3^4} = 3^{10-4} = 3^6
\][/tex]
Thus, the law used to simplify [tex]\(\frac{3^{10}}{3^4}\)[/tex] is the quotient of powers.
So, the correct choice is:
1. Quotient of powers
