Basic Math Examples

$81^{y} = \frac{1}{3}$

Step 1

Raise $3$ to the power of $1$ .

$81^{y} = \frac{1}{3^{1}}$

Step 2

Move $3^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$81^{y} = 3^{- 1}$

Step 3

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

$3^{4 y} = 3^{- 1}$

Step 4

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

$4 y = - 1$

Step 5

Divide each term in $4 y = - 1$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 y = - 1$ by $4$ .

$\frac{4 y}{4} = \frac{- 1}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 1}{4}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 1}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$y = - \frac{1}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{1}{4}$

Decimal Form:

$y = - 0.25$