Trigonometry Examples

$6 x^{\frac{5}{8}} - 18 = 100663278$

Step 1

Move all terms not containing $x$ to the right side of the equation.

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Step 1.1

Add $18$ to both sides of the equation.

$6 x^{\frac{5}{8}} - 100663278 = 18$

Step 1.2

Add $100663278$ to both sides of the equation.

$6 x^{\frac{5}{8}} = 18 + 100663278$

Step 1.3

Add $18$ and $100663278$ .

$6 x^{\frac{5}{8}} = 100663296$

Step 2

Raise each side of the equation to the power of $\frac{8}{5}$ to eliminate the fractional exponent on the left side.

${(6 x^{\frac{5}{8}})}^{\frac{8}{5}} = 100663296^{\frac{8}{5}}$

Step 3

Simplify the left side.

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Step 3.1

Simplify ${(6 x^{\frac{5}{8}})}^{\frac{8}{5}}$ .

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Step 3.1.1

Apply the product rule to $6 x^{\frac{5}{8}}$ .

$6^{\frac{8}{5}} {(x^{\frac{5}{8}})}^{\frac{8}{5}} = 100663296^{\frac{8}{5}}$

Step 3.1.2

Multiply the exponents in ${(x^{\frac{5}{8}})}^{\frac{8}{5}}$ .

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Step 3.1.2.1

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

$6^{\frac{8}{5}} x^{\frac{5}{8} \cdot \frac{8}{5}} = 100663296^{\frac{8}{5}}$

Step 3.1.2.2

Cancel the common factor of $5$ .

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Step 3.1.2.2.1

Cancel the common factor.

$6^{\frac{8}{5}} x^{\frac{5}{8} \cdot \frac{8}{5}} = 100663296^{\frac{8}{5}}$

Step 3.1.2.2.2

Rewrite the expression.

$6^{\frac{8}{5}} x^{\frac{1}{8} \cdot 8} = 100663296^{\frac{8}{5}}$

Step 3.1.2.3

Cancel the common factor of $8$ .

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Step 3.1.2.3.1

Cancel the common factor.

$6^{\frac{8}{5}} x^{\frac{1}{8} \cdot 8} = 100663296^{\frac{8}{5}}$

Step 3.1.2.3.2

Rewrite the expression.

$6^{\frac{8}{5}} x^{1} = 100663296^{\frac{8}{5}}$

Step 3.1.3

Simplify.

$6^{\frac{8}{5}} x = 100663296^{\frac{8}{5}}$

Step 3.1.4

Reorder factors in $6^{\frac{8}{5}} x$ .

$x \cdot 6^{\frac{8}{5}} = 100663296^{\frac{8}{5}}$

Step 4

Divide each term in $x \cdot 6^{\frac{8}{5}} = 100663296^{\frac{8}{5}}$ by $6^{\frac{8}{5}}$ and simplify.

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Step 4.1

Divide each term in $x \cdot 6^{\frac{8}{5}} = 100663296^{\frac{8}{5}}$ by $6^{\frac{8}{5}}$ .

$\frac{x \cdot 6^{\frac{8}{5}}}{6^{\frac{8}{5}}} = \frac{100663296^{\frac{8}{5}}}{6^{\frac{8}{5}}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor.

$\frac{x \cdot 6^{\frac{8}{5}}}{6^{\frac{8}{5}}} = \frac{100663296^{\frac{8}{5}}}{6^{\frac{8}{5}}}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{100663296^{\frac{8}{5}}}{6^{\frac{8}{5}}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Use the power of quotient rule $\frac{a^{m}}{b^{m}} = {(\frac{a}{b})}^{m}$ .

$x = {(\frac{100663296}{6})}^{\frac{8}{5}}$

Step 4.3.2

Divide $100663296$ by $6$ .

$x = 16777216^{\frac{8}{5}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 16777216^{\frac{8}{5}}$

Decimal Form:

$x = 362703572709.304$