To simplify the expression [tex]\( m^3 \times m^6 \)[/tex], we use the laws of exponents. One of the fundamental properties of exponents is:
[tex]\[ a^m \times a^n = a^{m+n} \][/tex]
This property states that when you multiply two expressions with the same base, you add their exponents.
Here, the base is [tex]\( m \)[/tex], and the exponents are 3 and 6. Therefore, we can apply this property as follows:
[tex]\[ m^3 \times m^6 = m^{3+6} \][/tex]
Now, simply add the exponents:
[tex]\[ 3 + 6 = 9 \][/tex]
So,
[tex]\[ m^3 \times m^6 = m^9 \][/tex]
Therefore, the simplified expression is [tex]\( m^9 \)[/tex].
