Algebra Examples

$\frac{5^{4}}{5^{3}} = 5^{b}$

Step 1

Rewrite the equation as $5^{b} = \frac{5^{4}}{5^{3}}$ .

$5^{b} = \frac{5^{4}}{5^{3}}$

Step 2

Move $5^{3}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$5^{b} = 5^{4} \cdot 5^{- 3}$

Step 3

Multiply $5^{4}$ by $5^{- 3}$ by adding the exponents.

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Step 3.1

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

$5^{b} = 5^{4 - 3}$

Step 3.2

Subtract $3$ from $4$ .

$5^{b} = 5^{1}$

Step 4

Simplify $5^{1}$ .

$5^{b} = 5$

Step 5

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

$5^{b} = 5^{1}$

Step 6

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

$b = 1$