Solve (2/5)^-3*(15/7)^-5=(a/b)

$$( \frac { 2 } { 5 } ) ^ { - 3 } \times ( \frac { 15 } { 7 } ) ^ { - 5 } = ( \frac { a } { b } )$$

Solve for a

$$a=\frac{16807b}{48600}$$

$$b\neq 0$$

Solution Steps

Multiply both sides of the equation by b.

$$\left(\frac{2}{5}\right)^{-3}\times \left(\frac{15}{7}\right)^{-5}b=a$$

Calculate \frac{2}{5} to the power of -3 and get \frac{125}{8}.

$$\frac{125}{8}\times \left(\frac{15}{7}\right)^{-5}b=a$$

Calculate \frac{15}{7} to the power of -5 and get \frac{16807}{759375}.

$$\frac{125}{8}\times \frac{16807}{759375}b=a$$

Multiply \frac{125}{8} and \frac{16807}{759375} to get \frac{16807}{48600}.

$$\frac{16807}{48600}b=a$$

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

$$a=\frac{16807}{48600}b$$

Solve for b

$$b=\frac{48600a}{16807}$$

$$a\neq 0$$

Steps for Solving Linear Equation

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

$$\left(\frac{2}{5}\right)^{-3}\times \left(\frac{15}{7}\right)^{-5}b=a$$

Calculate \frac{2}{5} to the power of -3 and get \frac{125}{8}.

$$\frac{125}{8}\times \left(\frac{15}{7}\right)^{-5}b=a$$

Calculate \frac{15}{7} to the power of -5 and get \frac{16807}{759375}.

$$\frac{125}{8}\times \frac{16807}{759375}b=a$$

Multiply \frac{125}{8} and \frac{16807}{759375} to get \frac{16807}{48600}.

$$\frac{16807}{48600}b=a$$

Divide both sides of the equation by \frac{16807}{48600}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{16807}{48600}b}{\frac{16807}{48600}}=\frac{a}{\frac{16807}{48600}}$$

Dividing by \frac{16807}{48600} undoes the multiplication by \frac{16807}{48600}.

$$b=\frac{a}{\frac{16807}{48600}}$$

Divide a by \frac{16807}{48600} by multiplying a by the reciprocal of \frac{16807}{48600}.

$$b=\frac{48600a}{16807}$$

Variable b cannot be equal to 0.

$$b=\frac{48600a}{16807}\text{, }b\neq 0$$