Question

I didn’t understand I’m freaking out over here can anybody help please

Answer 1

In our first equation, we can notice:

$(x^m*x^2)=x^{2+m}$

and

$(x^{m+2})^3*k^{15}=x^{21} *k^{15} \implies \\ x^{m+2}=x^{21}$

So, using the fact that $x^{y}=x^z \implies y=z$, we have:

$m+2=21 \implies\\ m=19$

In our second equation, we have:

$(x^3*y^2)(\frac{x^2y^3*z^m}{z^{-5}})=x^5y^5z$

So, using the exponent rules, we get:

$(x^3*y^2)(\frac{x^2y^3*z^m}{z^{-5}})=\\ x^{2+3}*y^{3+2}*z^{m-(-5)}=\\x^5*y^5*z^{m+5}$

So, we can cross out the common factors in each to give us:

$z^{m+5}=z \implies\\ z^{m+5}=z^1 \implies \\ m+5=1 \implies \\ m=-4$

So, using the exponent rules, we found the m values in both equations.