Answer:
[tex]\frac{81}{m^7}[/tex]
Step-by-step explanation:
We have a certain expression and are asked to find its equivalent with the answers provided :
[tex](3m^{-4} )^3(3m^5)[/tex]
Remove the parenthesis around 3m^5 :
[tex](3m^{-4} )^3*3m^5[/tex]
Do the exponent rule for outside and inside exponent parenthesis :
[tex](3m^{-4*3} )[/tex]
[tex]3^3m^{-12} *3m^5[/tex]
Apply addition exponent rule :
[tex]m^{-12} *3^{3+1} m^5[/tex]
Add :
[tex]m^{-12} *3^4m^5[/tex]
Apply the addition rule for -12 + 5 :
[tex]3^{4} m^{-7}[/tex]
Apply negative exponent rule for m^-7 :
[tex]3^4*\frac{1}{m^7}[/tex]
Multiply the fractions :
[tex]\frac{1*3^4}{m^7}[/tex]
[tex]\frac{81}{m^7}[/tex]
