Solve for n (3^4)÷(3^n)=9

$3^{4} \div 3^{n} = 9$

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

$3^{4} \cdot 3^{- n} = 9$

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

$3^{4 - n} = 9$

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

$3^{4 - n} = 3^{2}$

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

$4 - n = 2$

Solve for $n$ .

Tap for more steps…

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

Tap for more steps…

Subtract $4$ from both sides of the equation.

$- n = 2 - 4$

Subtract $4$ from $2$ .

$- n = - 2$

Multiply each term in $- n = - 2$ by $- 1$

Tap for more steps…

Multiply each term in $- n = - 2$ by $- 1$ .

$(- n) \cdot - 1 = (- 2) \cdot - 1$

Multiply $(- n) \cdot - 1$ .

Tap for more steps…

Multiply $- 1$ by $- 1$ .

$1 n = (- 2) \cdot - 1$

Multiply $n$ by $1$ .

$n = (- 2) \cdot - 1$

Multiply $- 2$ by $- 1$ .

$n = 2$

Solve for n (3^4)÷(3^n)=9

Our Professionals