Algebra Examples

$\frac{1}{k} = (7.3 \times 10^{8}) \times (2 \times 10^{- 5}) + \frac{1}{1 \times 10^{- 4}}$

Step 1

Simplify $7.3 \cdot 10^{8} \cdot 2 \cdot 10^{- 5} + \frac{1}{1 \cdot 10^{- 4}}$ .

Tap for more steps...

Step 1.1

Multiply $7.3$ by $2$ .

$\frac{1}{k} = 14.6 (10^{8} \cdot 10^{- 5}) + \frac{1}{1 \cdot 10^{- 4}}$

Step 1.2

Multiply $10^{8}$ by $10^{- 5}$ by adding the exponents.

Tap for more steps...

Step 1.2.1

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

$\frac{1}{k} = 14.6 \cdot 10^{8 - 5} + \frac{1}{1 \cdot 10^{- 4}}$

Step 1.2.2

Subtract $5$ from $8$ .

$\frac{1}{k} = 14.6 \cdot 10^{3} + \frac{1}{1 \cdot 10^{- 4}}$

Step 1.3

Divide using scientific notation.

Tap for more steps...

Step 1.3.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$\frac{1}{k} = 14.6 \cdot 10^{3} + (\frac{1}{1}) (\frac{1}{10^{- 4}})$

Step 1.3.2

Divide $1$ by $1$ .

$\frac{1}{k} = 14.6 \cdot 10^{3} + 1 \frac{1}{10^{- 4}}$

Step 1.3.3

Move $10^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{1}{k} = 14.6 \cdot 10^{3} + 1 \cdot 10^{4}$

Step 1.4

Move the decimal point in $14.6$ to the left by $1$ place and increase the power of $10^{3}$ by $1$ .

$\frac{1}{k} = 1.46 \cdot 10^{4} + 1 \cdot 10^{4}$

Step 1.5

Factor $10^{4}$ out of $1.46 \cdot 10^{4} + 1 \cdot 10^{4}$ .

$\frac{1}{k} = (1.46 + 1) \cdot 10^{4}$

Step 1.6

Add $1.46$ and $1$ .

$\frac{1}{k} = 2.46 \cdot 10^{4}$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$k, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$k$

Step 3

Multiply each term in $\frac{1}{k} = 2.46 \cdot 10^{4}$ by $k$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{1}{k} = 2.46 \cdot 10^{4}$ by $k$ .

$\frac{1}{k} k = 2.46 \cdot 10^{4} k$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $k$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{1}{k} k = 2.46 \cdot 10^{4} k$

Step 3.2.1.2

Rewrite the expression.

$1 = 2.46 \cdot 10^{4} k$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

Rewrite the equation as $2.46 \cdot 10^{4} k = 1$ .

$2.46 \cdot 10^{4} k = 1$

Step 4.2

Divide each term in $2.46 \cdot 10^{4} k = 1$ by $2.46 \cdot 10^{4}$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $2.46 \cdot 10^{4} k = 1$ by $2.46 \cdot 10^{4}$ .

$\frac{2.46 \cdot 10^{4} k}{2.46 \cdot 10^{4}} = \frac{1}{2.46 \cdot 10^{4}}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $2.46$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{2.46 \cdot 10^{4} k}{2.46 \cdot 10^{4}} = \frac{1}{2.46 \cdot 10^{4}}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{10^{4} k}{10^{4}} = \frac{1}{2.46 \cdot 10^{4}}$

Step 4.2.2.2

Cancel the common factor of $10^{4}$ .

Tap for more steps...

Step 4.2.2.2.1

Cancel the common factor.

$\frac{10^{4} k}{10^{4}} = \frac{1}{2.46 \cdot 10^{4}}$

Step 4.2.2.2.2

Divide $k$ by $1$ .

$k = \frac{1}{2.46 \cdot 10^{4}}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide using scientific notation.

Tap for more steps...

Step 4.2.3.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$k = (\frac{1}{2.46}) (\frac{1}{10^{4}})$

Step 4.2.3.1.2

Divide $1$ by $2.46$ .

$k = 0.\overline{40650} \frac{1}{10^{4}}$

Step 4.2.3.1.3

Move $10^{4}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$k = 0.\overline{40650} \cdot 10^{- 4}$

Step 4.2.3.2

Move the decimal point in $0.\overline{40650}$ to the right by $1$ place and decrease the power of $10^{- 4}$ by $1$ .

$k = 4.\overline{06504} \cdot 10^{- 5}$