Algebra Examples

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

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

Step 1

Simplify

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

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

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Step 1.1

Multiply

7.3

$7.3$ by

2

$2$ .

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

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

Step 1.2

Multiply

10^{8}

$10^{8}$ by

10^{- 5}

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

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Step 1.2.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 1.2.2

Subtract

5

$5$ from

8

$8$ .

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

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

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

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

Step 1.3

Divide using scientific notation.

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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}})

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

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.

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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.

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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.

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Step 3.2.1

Cancel the common factor of

$k$ .

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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.

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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.

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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.

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Step 4.2.2.1

Cancel the common factor of

$2.46$ .

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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

$10^{4}$ .

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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.

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Step 4.2.3.1

Divide using scientific notation.

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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

$1$ .

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