Solve for a (8^-55)/(8^a)=8^-43

$\frac{8^{- 55}}{8^{a}} = 8^{- 43}$

Step 1

Move $8^{a}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$8^{- 55} \cdot 8^{- a} = 8^{- 43}$

Step 2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8^{- 55 - a} = 8^{- 43}$

Step 3

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

$- 55 - a = - 43$

Step 4

Solve for $a$ .

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

Add $55$ to both sides of the equation.

$- a = - 43 + 55$

Add $- 43$ and $55$ .

$- a = 12$

Divide each term in $- a = 12$ by $- 1$ and simplify.

Divide each term in $- a = 12$ by $- 1$ .

$\frac{- a}{- 1} = \frac{12}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{a}{1} = \frac{12}{- 1}$

Divide $a$ by $1$ .

$a = \frac{12}{- 1}$

Simplify the right side.

Divide $12$ by $- 1$ .

$a = - 12$