Question

-2/3 to the power of -3 divided by x = 4/27 to the power of -2

Answer 1

$(\frac{-2}{3})^{-3} \div x=(\frac{4}{27})^{-2}$

Simplifies to:

$\frac{-27}{8x}=\frac{289}{16}$

Let's solve your equation step-by-step.

$\frac{-27}{8x}=\frac{729}{16}$

Step 1: Cross-multiply.

$\frac{-27}{8x}=\frac{729}{16}$

$(-27)\times (16)=729\times 8x$

$-432=5832x$

Step 2: Flip the equation.

$5832x=-432$

Step 3: Divide both sides by 5832.

$\frac{5831x}{5832}=\frac{-432}{5832}$

$x=\frac{-2}{27}$

Verification if $x=\frac{-2}{27}$

$(\frac{-2}{3})^{-3} \div x=(\frac{4}{27})^{-2}$

$(\frac{-2}{3})^{-3}\div \frac{-2}{27}$

$\frac{27}{-8}\div \frac{-2}{27}$

$\frac{-27}{8}\times \frac{-27}{2}$

$\frac{729}{16}$

${\frac{729}{16} =(\frac{27}{4}) ^2=(\frac{4}{27}) ^{-2}$

∴$x=\frac{-2}{27}$ in the equation ⇒ $(\frac{-2}{3})^{-3} \div x=(\frac{4}{27})^{-2}$