Basic Math Examples

$36^{a + 2} = {(\frac{1}{216})}^{3 a}$

Step 1

Apply the product rule to $\frac{1}{216}$ .

$36^{a + 2} = \frac{1^{3 a}}{216^{3 a}}$

Step 2

One to any power is one.

$36^{a + 2} = \frac{1}{216^{3 a}}$

Step 3

Move $216^{3 a}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$36^{a + 2} = 216^{- 3 a}$

Step 4

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

$6^{2 (a + 2)} = 6^{3 (- 3 a)}$

Step 5

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

$2 (a + 2) = 3 (- 3 a)$

Step 6

Solve for $a$ .

Tap for more steps...

Step 6.1

Simplify $2 (a + 2)$ .

Tap for more steps...

Step 6.1.1

Rewrite.

$0 + 0 + 2 (a + 2) = 3 (- 3 a)$

Step 6.1.2

Simplify by adding zeros.

$2 (a + 2) = 3 (- 3 a)$

Step 6.1.3

Apply the distributive property.

$2 a + 2 \cdot 2 = 3 (- 3 a)$

Step 6.1.4

Multiply $2$ by $2$ .

$2 a + 4 = 3 (- 3 a)$

Step 6.2

Multiply $- 3$ by $3$ .

$2 a + 4 = - 9 a$

Step 6.3

Move all terms containing $a$ to the left side of the equation.

Tap for more steps...

Step 6.3.1

Add $9 a$ to both sides of the equation.

$2 a + 4 + 9 a = 0$

Step 6.3.2

Add $2 a$ and $9 a$ .

$11 a + 4 = 0$

Step 6.4

Subtract $4$ from both sides of the equation.

$11 a = - 4$

Step 6.5

Divide each term in $11 a = - 4$ by $11$ and simplify.

Tap for more steps...

Step 6.5.1

Divide each term in $11 a = - 4$ by $11$ .

$\frac{11 a}{11} = \frac{- 4}{11}$

Step 6.5.2

Simplify the left side.

Tap for more steps...

Step 6.5.2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 6.5.2.1.1

Cancel the common factor.

$\frac{11 a}{11} = \frac{- 4}{11}$

Step 6.5.2.1.2

Divide $a$ by $1$ .

$a = \frac{- 4}{11}$

Step 6.5.3

Simplify the right side.

Tap for more steps...

Step 6.5.3.1

Move the negative in front of the fraction.

$a = - \frac{4}{11}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = - \frac{4}{11}$

Decimal Form:

$a = - 0.\overline{36}$