Question

1/(2/7)^8*1/(7/2)^2=(2/7)^2x find x

Answer 1

Answer:

-3

Step-by-step explanation:

We are given that, $\frac{1}{(\frac{2}{7} )^{8} } *\frac{1}{(\frac{7}{2} )^{2} } =(\frac{2}{7} )^{2x}$.

We have to solve the equation for x.

Now, $\frac{1}{(\frac{2}{7} )^{8} } *\frac{1}{(\frac{7}{2} )^{2} } =(\frac{2}{7} )^{2x}$

[Here we have to apply the formulas, $\frac{1}{a^{n} } =a^{-n}$ and, $\frac{1}{(\frac{a}{b} )^{n} } =(\frac{b}{a} )^{n}$]

⇒ $(\frac{2}{7} )^{-8} *(\frac{2}{7} )^{2} =(\frac{2}{7} )^{2x}$

[Here we have to apply the formula $a^{m} *a^{n} =a^{m+n}$]

⇒ $(\frac{2}{7} )^{-6} =(\frac{2}{7} )^{2x}$

Since, the base are same, comparing the power term on both sides we get

2x=-6

⇒ x=-3 (Answer)