Question

Complete the equation, by supplying the missing exponent. m•n2•m3= m 11n2

Answer 1

Given:

Consider the given equation is:

$m^?\cdot n^2\cdot m^3=m^{11}\cdot n^2$

To find:

The missing exponent.

Solution:

Let x be the missing exponent. Then the given equation can be written as

$m^x\cdot n^2\cdot m^3=m^{11}\cdot n^2$

It can be rewritten as:

$(m^x\cdot m^3)\cdot n^2=m^{11}\cdot n^2$

$m^{x+3}\cdot n^2=m^{11}\cdot n^2$      $[\because a^ma^n=a^{m+n}]$

On comparing the coefficient of m, we get

$x+3=11$

$x=11-3$

$x=8$

Therefore, the value of the missing exponent is 8. So, the complete equation is $m^8\cdot n^2\cdot m^3=m^{11}\cdot n^2$.