Solve (1/125)^(-5x 1)=(1/25)^(-x-5)

Evaluate

(\frac{1}{125})^{- 5 x \times 1} = (\frac{1}{25})^{- x - 5}

Multiply the terms

(\frac{1}{125})^{- 5 x} = (\frac{1}{25})^{- x - 5}

Rewrite the expression

More Steps

(\frac{1}{5})^{- 15 x} = (\frac{1}{25})^{- x - 5}

Rewrite the expression

More Steps

(\frac{1}{5})^{- 15 x} = (\frac{1}{5})^{- 2 x - 10}

Since the bases are the same,set the exponents equal

- 15 x = - 2 x - 10

Move the variable to the left side

- 15 x + 2 x = - 10

Add the terms

More Steps

- 13 x = - 10

Change the signs on both sides of the equation

13 x = 10

Divide both sides

\frac{13 x}{13} = \frac{10}{13}

Solution

x = \frac{10}{13}

Alternative Form

x = 0. \dot{7} 6923 \dot{0}

Solve the equation