Question

The equation (m^5/6) (m^1/6) ^7 =m^x what is the value of x that makes the equation true?​

Answer 1

Answer:

2

Step-by-step explanation:

We have the equation

$m^{5/6}(m^{1/6})^7=m^x$

The exponent rules to be used are

$a^x\times a^y=a^{x+y}$

$(a^{x})^y=a^{xy}$

$m^{5/6}(m)^{7/6}=m^x\\\Rightarrow m^{\dfrac{5}{6}+\dfrac{7}{6}}=m^x\\\Rightarrow m^{\dfrac{5+7}{6}}=m^x\\\Rightarrow m^{\dfrac{12}{6}}=m^x\\\Rightarrow m^{2}=m^x$

Comparing the exponents we get

$x=2$

So, the value of $x=2$ makes the equation true.