Basic Math Examples

$5^{y - 1} = \frac{1}{25}$

Step 1

Raise $25$ to the power of $1$ .

$5^{y - 1} = \frac{1}{25^{1}}$

Step 2

Move $25^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5^{y - 1} = 25^{- 1}$

Step 3

Create equivalent expressions in the equation that all have equal bases.

$5^{y - 1} = 5^{- 2}$

Step 4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$y - 1 = - 2$

Step 5

Move all terms not containing $y$ to the right side of the equation.

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Step 5.1

Add $1$ to both sides of the equation.

$y = - 2 + 1$

Step 5.2

Add $- 2$ and $1$ .

$y = - 1$