Algebra Examples

$2 {(\frac{1}{49})}^{x - 2} = 14$

Step 1

Divide each term in $2 {(\frac{1}{49})}^{x - 2} = 14$ by $2$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $2 {(\frac{1}{49})}^{x - 2} = 14$ by $2$ .

$\frac{2 {(\frac{1}{49})}^{x - 2}}{2} = \frac{14}{2}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{2 {(\frac{1}{49})}^{x - 2}}{2} = \frac{14}{2}$

Step 1.2.1.2

Divide ${(\frac{1}{49})}^{x - 2}$ by $1$ .

${(\frac{1}{49})}^{x - 2} = \frac{14}{2}$

Step 1.2.2

Simplify the expression.

Tap for more steps...

Step 1.2.2.1

Apply the product rule to $\frac{1}{49}$ .

$\frac{1^{x - 2}}{49^{x - 2}} = \frac{14}{2}$

Step 1.2.2.2

One to any power is one.

$\frac{1}{49^{x - 2}} = \frac{14}{2}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $14$ by $2$ .

$\frac{1}{49^{x - 2}} = 7$

Step 2

Move $49^{x - 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$49^{- (x - 2)} = 7$

Step 3

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

$7^{2 (- (x - 2))} = 7^{1}$

Step 4

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

$2 (- (x - 2)) = 1$

Step 5

Solve for $x$ .

Tap for more steps...

Step 5.1

Simplify.

Tap for more steps...

Step 5.1.1

Apply the distributive property.

$2 (- x - - 2) = 1$

Step 5.1.2

Multiply $- 1$ by $- 2$ .

$2 (- x + 2) = 1$

Step 5.2

Divide each term in $2 (- x + 2) = 1$ by $2$ and simplify.

Tap for more steps...

Step 5.2.1

Divide each term in $2 (- x + 2) = 1$ by $2$ .

$\frac{2 (- x + 2)}{2} = \frac{1}{2}$

Step 5.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 (- x + 2)}{2} = \frac{1}{2}$

Step 5.2.2.1.2

Divide $- x + 2$ by $1$ .

$- x + 2 = \frac{1}{2}$

Step 5.3

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

Tap for more steps...

Step 5.3.1

Subtract $2$ from both sides of the equation.

$- x = \frac{1}{2} - 2$

Step 5.3.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- x = \frac{1}{2} - 2 \cdot \frac{2}{2}$

Step 5.3.3

Combine $- 2$ and $\frac{2}{2}$ .

$- x = \frac{1}{2} + \frac{- 2 \cdot 2}{2}$

Step 5.3.4

Combine the numerators over the common denominator.

$- x = \frac{1 - 2 \cdot 2}{2}$

Step 5.3.5

Simplify the numerator.

Tap for more steps...

Step 5.3.5.1

Multiply $- 2$ by $2$ .

$- x = \frac{1 - 4}{2}$

Step 5.3.5.2

Subtract $4$ from $1$ .

$- x = \frac{- 3}{2}$

Step 5.3.6

Move the negative in front of the fraction.

$- x = - \frac{3}{2}$

Step 5.4

Divide each term in $- x = - \frac{3}{2}$ by $- 1$ and simplify.

Tap for more steps...

Step 5.4.1

Divide each term in $- x = - \frac{3}{2}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \frac{3}{2}}{- 1}$

Step 5.4.2

Simplify the left side.

Tap for more steps...

Step 5.4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \frac{3}{2}}{- 1}$

Step 5.4.2.2

Divide $x$ by $1$ .

$x = \frac{- \frac{3}{2}}{- 1}$

Step 5.4.3

Simplify the right side.

Tap for more steps...

Step 5.4.3.1

Dividing two negative values results in a positive value.

$x = \frac{\frac{3}{2}}{1}$

Step 5.4.3.2

Divide $\frac{3}{2}$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$