Finite Math Examples

$6 = 2 \cdot k^{0.5}$

Step 1

Rewrite the equation as $2 \cdot k^{0.5} = 6$ .

$2 \cdot k^{0.5} = 6$

Step 2

Divide each term in $2 \cdot k^{0.5} = 6$ by $2$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $2 \cdot k^{0.5} = 6$ by $2$ .

$\frac{2 \cdot k^{0.5}}{2} = \frac{6}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{2 \cdot k^{0.5}}{2} = \frac{6}{2}$

Step 2.2.1.2

Divide $k^{0.5}$ by $1$ .

$k^{0.5} = \frac{6}{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Divide $6$ by $2$ .

$k^{0.5} = 3$

Step 3

Convert the decimal exponent to a fractional exponent.

Tap for more steps...

Step 3.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is $1$ number to the right of the decimal point, place the decimal number over $10^{1}$ $(10)$ . Next, add the whole number to the left of the decimal.

$k^{0 \frac{5}{10}} = 3$

Step 3.2

Reduce the fraction.

Tap for more steps...

Step 3.2.1

Convert $0 \frac{5}{10}$ to an improper fraction.

Tap for more steps...

Step 3.2.1.1

A mixed number is an addition of its whole and fractional parts.

$k^{0 + \frac{5}{10}} = 3$

Step 3.2.1.2

Add $0$ and $\frac{5}{10}$ .

$k^{\frac{5}{10}} = 3$

Step 3.2.2

Cancel the common factor of $5$ and $10$ .

Tap for more steps...

Step 3.2.2.1

Factor $5$ out of $5$ .

$k^{\frac{5 (1)}{10}} = 3$

Step 3.2.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.2.1

Factor $5$ out of $10$ .

$k^{\frac{5 \cdot 1}{5 \cdot 2}} = 3$

Step 3.2.2.2.2

Cancel the common factor.

$k^{\frac{5 \cdot 1}{5 \cdot 2}} = 3$

Step 3.2.2.2.3

Rewrite the expression.

$k^{\frac{1}{2}} = 3$

Step 4

Raise each side of the equation to the power of $\frac{1}{0.5}$ to eliminate the fractional exponent on the left side.

${(k^{\frac{1}{2}})}^{\frac{1}{0.5}} = 3^{\frac{1}{0.5}}$

Step 5

Simplify the exponent.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify ${(k^{\frac{1}{2}})}^{\frac{1}{0.5}}$ .

Tap for more steps...

Step 5.1.1.1

Multiply the exponents in ${(k^{\frac{1}{2}})}^{\frac{1}{0.5}}$ .

Tap for more steps...

Step 5.1.1.1.1

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

$k^{\frac{1}{2} \cdot \frac{1}{0.5}} = 3^{\frac{1}{0.5}}$

Step 5.1.1.1.2

Cancel the common factor of $0.5$ .

Tap for more steps...

Step 5.1.1.1.2.1

Factor $0.5$ out of $1$ .

$k^{\frac{0.5 (2)}{2} \cdot \frac{1}{0.5}} = 3^{\frac{1}{0.5}}$

Step 5.1.1.1.2.2

Cancel the common factor.

$k^{\frac{0.5 \cdot 2}{2} \cdot \frac{1}{0.5}} = 3^{\frac{1}{0.5}}$

Step 5.1.1.1.2.3

Rewrite the expression.

$k^{\frac{2}{2}} = 3^{\frac{1}{0.5}}$

Step 5.1.1.1.3

Divide $2$ by $2$ .

$k^{1} = 3^{\frac{1}{0.5}}$

Step 5.1.1.2

Simplify.

$k = 3^{\frac{1}{0.5}}$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $3^{\frac{1}{0.5}}$ .

Tap for more steps...

Step 5.2.1.1

Divide $1$ by $0.5$ .

$k = 3^{2}$

Step 5.2.1.2

Raise $3$ to the power of $2$ .

$k = 9$