Algebra Examples

$\frac{5^{6}}{5^{m}} = 5^{9}$

Step 1

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

$5^{6} \cdot 5^{- m} = 5^{9}$

Step 2

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

$5^{6 - m} = 5^{9}$

Step 3

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

$6 - m = 9$

Step 4

Solve for $m$ .

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Step 4.1

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

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Step 4.1.1

Subtract $6$ from both sides of the equation.

$- m = 9 - 6$

Step 4.1.2

Subtract $6$ from $9$ .

$- m = 3$

Step 4.2

Divide each term in $- m = 3$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- m = 3$ by $- 1$ .

$\frac{- m}{- 1} = \frac{3}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{m}{1} = \frac{3}{- 1}$

Step 4.2.2.2

Divide $m$ by $1$ .

$m = \frac{3}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $3$ by $- 1$ .

$m = - 3$