Solve for k 1/k=(7.310^8)(2.010^-5)+1/(1.0010^-4)

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

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

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

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

Multiply $7.3$ by $2$ .

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

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

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

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

Subtract $5$ from $8$ .

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

Divide using scientific notation.

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

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

Divide $1$ by $1$ .

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

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

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

Factor $10^{3}$ out of $1 \cdot 10^{4}$ .

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

Factor $10^{3}$ out of $14.6 \cdot 10^{3}$ .

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

Factor $10^{3}$ out of $10^{3} \cdot 14.6 + 10^{3} (1 \cdot 10)$ .

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

Simplify the expression.

Reorder $10^{3}$ and $14.6 + 1 \cdot 10$ .

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

Multiply $10$ by $1$ .

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

Add $14.6$ and $10$ .

$\frac{1}{k} = 24.6 \cdot 10^{3}$

Write $24.6 \cdot 10^{3}$ in proper scientific notation.

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

Find the LCD of the terms in the equation.

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

$k, 1, 1$

The LCM of one and any expression is the expression.

$k$

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

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

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

Simplify the left side.

Cancel the common factor of $k$ .

Cancel the common factor.

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

Rewrite the expression.

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

Solve the equation.

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $2.46$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Cancel the common factor.

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

Divide $k$ by $1$ .

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

Simplify the right side.

Divide using scientific notation.

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

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

Divide $1$ by $2.46$ .

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

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

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

Write $0.\overline{40650} \cdot 10^{- 4}$ in proper scientific notation.

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

Solve for k 1/k=(7.3*10^8)*(2.0*10^-5)+1/(1.00*10^-4)

Related Questions

Support LCMGCF.com by disabling your adblocker.

Solve for k 1/k=(7.310^8)(2.010^-5)+1/(1.0010^-4)