Given:
Consider the given equation is:
[tex]m^?\cdot n^2\cdot m^3=m^{11}\cdot n^2[/tex]
To find:
The missing exponent.
Solution:
Let x be the missing exponent. Then the given equation can be written as
[tex]m^x\cdot n^2\cdot m^3=m^{11}\cdot n^2[/tex]
It can be rewritten as:
[tex](m^x\cdot m^3)\cdot n^2=m^{11}\cdot n^2[/tex]
[tex]m^{x+3}\cdot n^2=m^{11}\cdot n^2[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
On comparing the coefficient of m, we get
[tex]x+3=11[/tex]
[tex]x=11-3[/tex]
[tex]x=8[/tex]
Therefore, the value of the missing exponent is 8. So, the complete equation is [tex]m^8\cdot n^2\cdot m^3=m^{11}\cdot n^2[/tex].
