Basic Math Examples

$365^{2} = k {(93 (10^{6}))}^{3}$

Step 1

Rewrite the equation as $k {(93 \cdot 10^{6})}^{3} = 365^{2}$ .

$k {(93 \cdot 10^{6})}^{3} = 365^{2}$

Step 2

Move the decimal point in $93$ to the left by $1$ place and increase the power of $10^{6}$ by $1$ .

$k {(9.3 \cdot 10^{7})}^{3} = 365^{2}$

Step 3

Divide each term in $k {(9.3 \cdot 10^{7})}^{3} = 365^{2}$ by ${(9.3 \cdot 10^{7})}^{3}$ and simplify.

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Step 3.1

Divide each term in $k {(9.3 \cdot 10^{7})}^{3} = 365^{2}$ by ${(9.3 \cdot 10^{7})}^{3}$ .

$\frac{k {(9.3 \cdot 10^{7})}^{3}}{{(9.3 \cdot 10^{7})}^{3}} = \frac{365^{2}}{{(9.3 \cdot 10^{7})}^{3}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of ${(9.3 \cdot 10^{7})}^{3}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{k {(9.3 \cdot 10^{7})}^{3}}{{(9.3 \cdot 10^{7})}^{3}} = \frac{365^{2}}{{(9.3 \cdot 10^{7})}^{3}}$

Step 3.2.1.2

Divide $k$ by $1$ .

$k = \frac{365^{2}}{{(9.3 \cdot 10^{7})}^{3}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $365$ to the power of $2$ .

$k = \frac{133225}{{(9.3 \cdot 10^{7})}^{3}}$

Step 3.3.2

Simplify the denominator.

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Step 3.3.2.1

Apply the product rule to $9.3 \cdot 10^{7}$ .

$k = \frac{133225}{{9.3}^{3} \cdot {(10^{7})}^{3}}$

Step 3.3.2.2

Raise $9.3$ to the power of $3$ .

$k = \frac{133225}{804.357 \cdot {(10^{7})}^{3}}$

Step 3.3.2.3

Multiply the exponents in ${(10^{7})}^{3}$ .

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Step 3.3.2.3.1

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

$k = \frac{133225}{804.357 \cdot 10^{7 \cdot 3}}$

Step 3.3.2.3.2

Multiply $7$ by $3$ .

$k = \frac{133225}{804.357 \cdot 10^{21}}$

Step 3.3.2.4

Raise $10$ to the power of $21$ .

$k = \frac{133225}{804.357 \cdot 1000000000000000000000}$

Step 3.3.3

Reduce the expression by cancelling the common factors.

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Step 3.3.3.1

Multiply $804.357$ by $1000000000000000000000$ .

$k = \frac{133225}{804357000000000000000000}$

Step 3.3.3.2

Cancel the common factor of $133225$ and $804357000000000000000000$ .

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Step 3.3.3.2.1

Factor $25$ out of $133225$ .

$k = \frac{25 (5329)}{804357000000000000000000}$

Step 3.3.3.2.2

Cancel the common factors.

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Step 3.3.3.2.2.1

Factor $25$ out of $804357000000000000000000$ .

$k = \frac{25 \cdot 5329}{25 \cdot 32174280000000000000000}$

Step 3.3.3.2.2.2

Cancel the common factor.

$k = \frac{25 \cdot 5329}{25 \cdot 32174280000000000000000}$

Step 3.3.3.2.2.3

Rewrite the expression.

$k = \frac{5329}{32174280000000000000000}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$k = \frac{5329}{32174280000000000000000}$

Decimal Form:

$k = 1.65629192 \cdot 10^{- 19}$