Basic Math Examples

$- 2 - \frac{2}{6 \sqrt[543827]{644}}$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ and $6$ .

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Step 1.1.1

Factor $2$ out of $2$ .

$- 2 - \frac{2 (1)}{6 \sqrt[543827]{644}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $6 \sqrt[543827]{644}$ .

$- 2 - \frac{2 (1)}{2 (3 \sqrt[543827]{644})}$

Step 1.1.2.2

Cancel the common factor.

$- 2 - \frac{2 \cdot 1}{2 (3 \sqrt[543827]{644})}$

Step 1.1.2.3

Rewrite the expression.

$- 2 - \frac{1}{3 \sqrt[543827]{644}}$

Step 1.2

Multiply $\frac{1}{3 \sqrt[543827]{644}}$ by $\frac{{\sqrt[543827]{644}}^{543826}}{{\sqrt[543827]{644}}^{543826}}$ .

$- 2 - (\frac{1}{3 \sqrt[543827]{644}} \cdot \frac{{\sqrt[543827]{644}}^{543826}}{{\sqrt[543827]{644}}^{543826}})$

Step 1.3

Combine and simplify the denominator.

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Step 1.3.1

Multiply $\frac{1}{3 \sqrt[543827]{644}}$ by $\frac{{\sqrt[543827]{644}}^{543826}}{{\sqrt[543827]{644}}^{543826}}$ .

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 \sqrt[543827]{644} {\sqrt[543827]{644}}^{543826}}$

Step 1.3.2

Move $\sqrt[543827]{644}$ .

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 (\sqrt[543827]{644} {\sqrt[543827]{644}}^{543826})}$

Step 1.3.3

Raise $\sqrt[543827]{644}$ to the power of $1$ .

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 ({\sqrt[543827]{644}}^{1} {\sqrt[543827]{644}}^{543826})}$

Step 1.3.4

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

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 {\sqrt[543827]{644}}^{1 + 543826}}$

Step 1.3.5

Add $1$ and $543826$ .

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 {\sqrt[543827]{644}}^{543827}}$

Step 1.3.6

Rewrite ${\sqrt[543827]{644}}^{543827}$ as $644$ .

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Step 1.3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[543827]{644}$ as $644^{\frac{1}{543827}}$ .

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 {(644^{\frac{1}{543827}})}^{543827}}$

Step 1.3.6.2

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

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 \cdot 644^{\frac{1}{543827} \cdot 543827}}$

Step 1.3.6.3

Combine $\frac{1}{543827}$ and $543827$ .

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 \cdot 644^{\frac{543827}{543827}}}$

Step 1.3.6.4

Cancel the common factor of $543827$ .

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Step 1.3.6.4.1

Cancel the common factor.

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 \cdot 644^{\frac{543827}{543827}}}$

Step 1.3.6.4.2

Rewrite the expression.

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 \cdot 644^{1}}$

Step 1.3.6.5

Evaluate the exponent.

$- 2 - \frac{{\sqrt[543827]{644}}^{543826}}{3 \cdot 644}$

Step 1.4

Rewrite ${\sqrt[543827]{644}}^{543826}$ as $\sqrt[543827]{644^{543826}}$ .

$- 2 - \frac{\sqrt[543827]{644^{543826}}}{3 \cdot 644}$

Step 1.5

Multiply $3$ by $644$ .

$- 2 - \frac{\sqrt[543827]{644^{543826}}}{1932}$

Step 2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{1932}{1932}$ .

$- 2 \cdot \frac{1932}{1932} - \frac{\sqrt[543827]{644^{543826}}}{1932}$

Step 3

Combine $- 2$ and $\frac{1932}{1932}$ .

$\frac{- 2 \cdot 1932}{1932} - \frac{\sqrt[543827]{644^{543826}}}{1932}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{- 2 \cdot 1932 - \sqrt[543827]{644^{543826}}}{1932}$

Step 4.2

Multiply $- 2$ by $1932$ .

$\frac{- 3864 - \sqrt[543827]{644^{543826}}}{1932}$

Step 5

Rewrite $- 3864$ as $- 1 (3864)$ .

$\frac{- 1 (3864) - \sqrt[543827]{644^{543826}}}{1932}$

Step 6

Factor $- 1$ out of $- \sqrt[543827]{644^{543826}}$ .

$\frac{- 1 (3864) - (\sqrt[543827]{644^{543826}})}{1932}$

Step 7

Factor $- 1$ out of $- 1 (3864) - (\sqrt[543827]{644^{543826}})$ .

$\frac{- 1 (3864 + \sqrt[543827]{644^{543826}})}{1932}$

Step 8

Move the negative in front of the fraction.

$- \frac{3864 + \sqrt[543827]{644^{543826}}}{1932}$