Finite Math Examples

$9^{- 6 x + (3)} = 9^{3 \sqrt{9}}$

Step 1

Remove parentheses.

$9^{- 6 x + 3} = 9^{3 \sqrt{9}}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9}$ as $9^{\frac{1}{2}}$ .

$9^{- 6 x + 3} = 9^{3 \cdot 9^{\frac{1}{2}}}$

Step 3

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

$- 6 x + 3 = 3 \cdot 9^{\frac{1}{2}}$

Step 4

Solve for $x$ .

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Step 4.1

Simplify $3 \cdot 9^{\frac{1}{2}}$ .

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Step 4.1.1

Rewrite.

$- 6 x + 3 = 0 + 0 + 3 \cdot 9^{\frac{1}{2}}$

Step 4.1.2

Simplify the expression.

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Step 4.1.2.1

Rewrite $9$ as $3^{2}$ .

$- 6 x + 3 = 3 \cdot {(3^{2})}^{\frac{1}{2}}$

Step 4.1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 6 x + 3 = 3 \cdot 3^{2 (\frac{1}{2})}$

Step 4.1.3

Cancel the common factor of $2$ .

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Step 4.1.3.1

Cancel the common factor.

$- 6 x + 3 = 3 \cdot 3^{2 (\frac{1}{2})}$

Step 4.1.3.2

Rewrite the expression.

$- 6 x + 3 = 3 \cdot 3^{1}$

Step 4.1.4

Evaluate the exponent.

$- 6 x + 3 = 3 \cdot 3$

Step 4.1.5

Multiply $3$ by $3$ .

$- 6 x + 3 = 9$

Step 4.2

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

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Step 4.2.1

Subtract $3$ from both sides of the equation.

$- 6 x = 9 - 3$

Step 4.2.2

Subtract $3$ from $9$ .

$- 6 x = 6$

Step 4.3

Divide each term in $- 6 x = 6$ by $- 6$ and simplify.

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Step 4.3.1

Divide each term in $- 6 x = 6$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{6}{- 6}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 6$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{6}{- 6}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{- 6}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $6$ by $- 6$ .

$x = - 1$