Solve {left(frac{169/225right)}^-1}{x}={left(13/15right)}^-5

$$\frac{ { \left( \frac{ 169 }{ 225 } \right) }^{ -1 } }{ x } = { \left( \frac{ 13 }{ 15 } \right) }^{ -5 }$$

Solve for x

$$x=\frac{2197}{3375}\approx 0.650962963$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$\left(\frac{169}{225}\right)^{-1}=x\times \left(\frac{13}{15}\right)^{-5}$$

Calculate \frac{169}{225} to the power of -1 and get \frac{225}{169}.

$$\frac{225}{169}=x\times \left(\frac{13}{15}\right)^{-5}$$

Calculate \frac{13}{15} to the power of -5 and get \frac{759375}{371293}.

$$\frac{225}{169}=x\times \frac{759375}{371293}$$

Swap sides so that all variable terms are on the left hand side.

$$x\times \frac{759375}{371293}=\frac{225}{169}$$

Multiply both sides by \frac{371293}{759375}, the reciprocal of \frac{759375}{371293}.

$$x=\frac{225}{169}\times \frac{371293}{759375}$$

Multiply \frac{225}{169} and \frac{371293}{759375} to get \frac{2197}{3375}.

$$x=\frac{2197}{3375}$$