To simplify the expression [tex]\( x^5 \cdot x^7 \)[/tex], we use the property of exponents. The property states that when you multiply two expressions with the same base, you add their exponents.
Let's denote the expression as follows:
[tex]\[ x^5 \cdot x^7 \][/tex]
According to the property of exponents:
[tex]\[ x^a \cdot x^b = x^{a+b} \][/tex]
In our case, [tex]\( a = 5 \)[/tex] and [tex]\( b = 7 \)[/tex]. Therefore, we add the exponents:
[tex]\[ 5 + 7 = 12 \][/tex]
So, the expression simplifies to:
[tex]\[ x^{5+7} = x^{12} \][/tex]
Therefore, the simplified expression is:
[tex]\[ x^{12} \][/tex]
