Answer:
2
Step-by-step explanation:
We have the equation
[tex]m^{5/6}(m^{1/6})^7=m^x[/tex]
The exponent rules to be used are
[tex]a^x\times a^y=a^{x+y}[/tex]
[tex](a^{x})^y=a^{xy}[/tex]
[tex]m^{5/6}(m)^{7/6}=m^x\\\Rightarrow m^{\dfrac{5}{6}+\dfrac{7}{6}}=m^x\\\Rightarrow m^{\dfrac{5+7}{6}}=m^x\\\Rightarrow m^{\dfrac{12}{6}}=m^x\\\Rightarrow m^{2}=m^x[/tex]
Comparing the exponents we get
[tex]x=2[/tex]
So, the value of [tex]x=2[/tex] makes the equation true.
