Algebra Examples

$\frac{11^{x}}{11^{3}} = 11^{2}$

Step 1

Move $11^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$11^{x} \cdot 11^{- 3} = 11^{2}$

Step 2

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

$11^{x - 3} = 11^{2}$

Step 3

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

$x - 3 = 2$

Step 4

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

Tap for more steps...

Step 4.1

Add $3$ to both sides of the equation.

$x = 2 + 3$

Step 4.2

Add $2$ and $3$ .

$x = 5$