Basic Math Examples

$10 = 1.6 \cdot 10^{- 8} \cdot \frac{y}{1.9625}$

Step 1

Rewrite the equation as $1.6 \cdot 10^{- 8} \cdot \frac{y}{1.9625} = 10$ .

$1.6 \cdot 10^{- 8} \cdot \frac{y}{1.9625} = 10$

Step 2

Simplify.

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Step 2.1

Combine $1.6$ and $\frac{y}{1.9625}$ .

$10^{- 8} \cdot \frac{1.6 y}{1.9625} = 10$

Step 2.2

Combine $10^{- 8}$ and $\frac{1.6 y}{1.9625}$ .

$\frac{10^{- 8} (1.6 y)}{1.9625} = 10$

Step 2.3

Remove parentheses.

$\frac{10^{- 8} \cdot 1.6 y}{1.9625} = 10$

Step 3

Divide each term in $\frac{10^{- 8} \cdot (1.6 y)}{1.9625} = 10$ by $1.6 \cdot 10^{- 8}$ and simplify.

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Step 3.1

Divide each term in $\frac{10^{- 8} \cdot (1.6 y)}{1.9625} = 10$ by $1.6 \cdot 10^{- 8}$ .

$\frac{\frac{10^{- 8} \cdot (1.6 y)}{1.9625}}{1.6 \cdot 10^{- 8}} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Move $10^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\frac{10^{- 8} \cdot (1.6 y)}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2

Simplify the numerator.

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Step 3.2.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{\frac{1}{10^{8}} \cdot 1.6 y}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.2

Raise $10$ to the power of $8$ .

$\frac{\frac{\frac{1}{100000000} \cdot 1.6 y}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.3

Combine exponents.

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Step 3.2.2.3.1

Combine $\frac{1}{100000000}$ and $1.6$ .

$\frac{\frac{\frac{1.6}{100000000} y}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.3.2

Combine $\frac{1.6}{100000000}$ and $y$ .

$\frac{\frac{\frac{1.6 y}{100000000}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.4

Factor $1.6$ out of $1.6 y$ .

$\frac{\frac{\frac{1.6 (y)}{100000000}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.5

Factor $100000000$ out of $100000000$ .

$\frac{\frac{\frac{1.6 (y)}{100000000 (1)}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.6

Separate fractions.

$\frac{\frac{\frac{1.6}{100000000} \cdot \frac{y}{1}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.7

Divide $1.6$ by $100000000$ .

$\frac{\frac{0.00000001 \frac{y}{1}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.8

Cancel the common factor of $0.00000001$ .

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Step 3.2.2.8.1

Factor $0.00000001$ out of $1$ .

$\frac{\frac{0.00000001 \frac{y}{0.00000001 \cdot 62500000}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.8.2

Cancel the common factor.

$\frac{\frac{0.00000001 \frac{y}{0.00000001 \cdot 62500000}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.2.8.3

Rewrite the expression.

$\frac{\frac{\frac{y}{62500000}}{1.9625} \cdot 10^{8}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.3

Combine fractions.

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Step 3.2.3.1

Combine $\frac{\frac{y}{62500000}}{1.9625}$ and $10^{8}$ .

$\frac{\frac{\frac{y}{62500000} \cdot 10^{8}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.3.2

Combine $\frac{y}{62500000}$ and $10^{8}$ .

$\frac{\frac{\frac{y \cdot 10^{8}}{62500000}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.3.3

Raise $10$ to the power of $8$ .

$\frac{\frac{\frac{y \cdot 100000000}{62500000}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Reduce the expression $\frac{y \cdot 100000000}{62500000}$ by cancelling the common factors.

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Step 3.2.4.1.1

Factor $12500000$ out of $y \cdot 100000000$ .

$\frac{\frac{\frac{12500000 (y \cdot 8)}{62500000}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.4.1.2

Factor $12500000$ out of $62500000$ .

$\frac{\frac{\frac{12500000 (y \cdot 8)}{12500000 (5)}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.4.1.3

Cancel the common factor.

$\frac{\frac{\frac{12500000 (y \cdot 8)}{12500000 \cdot 5}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.4.1.4

Rewrite the expression.

$\frac{\frac{\frac{y \cdot 8}{5}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.4.2

Move $8$ to the left of $y$ .

$\frac{\frac{\frac{8 y}{5}}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5

Simplify the numerator.

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Step 3.2.5.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{8 y}{5} \cdot \frac{1}{1.9625}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.2

Divide $1$ by $1.9625$ .

$\frac{\frac{8 y}{5} \cdot 0.50955414}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.3

Multiply $\frac{8 y}{5} \cdot 0.50955414$ .

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Step 3.2.5.3.1

Combine $\frac{8 y}{5}$ and $0.50955414$ .

$\frac{\frac{8 y \cdot 0.50955414}{5}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.3.2

Multiply $0.50955414$ by $8$ .

$\frac{\frac{4.07643312 y}{5}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.4

Factor $4.07643312$ out of $4.07643312 y$ .

$\frac{\frac{4.07643312 (y)}{5}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.5

Factor $5$ out of $5$ .

$\frac{\frac{4.07643312 (y)}{5 (1)}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.6

Separate fractions.

$\frac{\frac{4.07643312}{5} \cdot \frac{y}{1}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.7

Divide $4.07643312$ by $5$ .

$\frac{0.81528662 \frac{y}{1}}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.5.8

Divide $y$ by $1$ .

$\frac{0.81528662 y}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.6

Simplify with factoring out.

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Step 3.2.6.1

Factor $0.81528662$ out of $0.81528662 y$ .

$\frac{0.81528662 (y)}{1.6} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.6.2

Factor $1.6$ out of $1.6$ .

$\frac{0.81528662 (y)}{1.6 (1)} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.7

Separate fractions.

$\frac{0.81528662}{1.6} \cdot \frac{y}{1} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.8

Divide $0.81528662$ by $1.6$ .

$0.50955414 \frac{y}{1} = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.2.9

Divide $y$ by $1$ .

$0.50955414 y = \frac{10}{1.6 \cdot 10^{- 8}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide using scientific notation.

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Step 3.3.1.1

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

$0.50955414 y = (\frac{10}{1.6}) (\frac{1}{10^{- 8}})$

Step 3.3.1.2

Divide $10$ by $1.6$ .

$0.50955414 y = 6.25 \frac{1}{10^{- 8}}$

Step 3.3.1.3

Move $10^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$0.50955414 y = 6.25 \cdot 10^{8}$

Step 4

Divide each term in $0.50955414 y = 6.25 \cdot 10^{8}$ by $0.50955414$ and simplify.

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Step 4.1

Divide each term in $0.50955414 y = 6.25 \cdot 10^{8}$ by $0.50955414$ .

$\frac{0.50955414 y}{0.50955414} = \frac{6.25 \cdot 10^{8}}{0.50955414}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.50955414$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.50955414 y}{0.50955414} = \frac{6.25 \cdot 10^{8}}{0.50955414}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{6.25 \cdot 10^{8}}{0.50955414}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide using scientific notation.

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Step 4.3.1.1

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

$y = (\frac{6.25}{0.50955414}) (\frac{10^{8}}{1})$

Step 4.3.1.2

Divide $6.25$ by $0.50955414$ .

$y = 12.265624\overline{9} \frac{10^{8}}{1}$

Step 4.3.1.3

Divide $10^{8}$ by $1$ .

$y = 12.265624\overline{9} \cdot 10^{8}$

Step 4.3.2

Move the decimal point in $12.265624\overline{9}$ to the left by $1$ place and increase the power of $10^{8}$ by $1$ .

$y = 1.2265625 \cdot 10^{9}$

Step 5

The result can be shown in multiple forms.

Scientific Notation:

$y = 1.2265625 \cdot 10^{9}$

Expanded Form:

$y = 1226562500$