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

Sagot :

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].

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