Trigonometry Examples

$3 x^{\frac{7}{3}} - 33 = 0$

Step 1

Add $33$ to both sides of the equation.

$3 x^{\frac{7}{3}} = 33$

Step 2

Raise each side of the equation to the power of $\frac{3}{7}$ to eliminate the fractional exponent on the left side.

${(3 x^{\frac{7}{3}})}^{\frac{3}{7}} = 33^{\frac{3}{7}}$

Step 3

Simplify the left side.

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Step 3.1

Simplify ${(3 x^{\frac{7}{3}})}^{\frac{3}{7}}$ .

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Step 3.1.1

Apply the product rule to $3 x^{\frac{7}{3}}$ .

$3^{\frac{3}{7}} {(x^{\frac{7}{3}})}^{\frac{3}{7}} = 33^{\frac{3}{7}}$

Step 3.1.2

Multiply the exponents in ${(x^{\frac{7}{3}})}^{\frac{3}{7}}$ .

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Step 3.1.2.1

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

$3^{\frac{3}{7}} x^{\frac{7}{3} \cdot \frac{3}{7}} = 33^{\frac{3}{7}}$

Step 3.1.2.2

Cancel the common factor of $7$ .

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Step 3.1.2.2.1

Cancel the common factor.

$3^{\frac{3}{7}} x^{\frac{7}{3} \cdot \frac{3}{7}} = 33^{\frac{3}{7}}$

Step 3.1.2.2.2

Rewrite the expression.

$3^{\frac{3}{7}} x^{\frac{1}{3} \cdot 3} = 33^{\frac{3}{7}}$

Step 3.1.2.3

Cancel the common factor of $3$ .

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Step 3.1.2.3.1

Cancel the common factor.

$3^{\frac{3}{7}} x^{\frac{1}{3} \cdot 3} = 33^{\frac{3}{7}}$

Step 3.1.2.3.2

Rewrite the expression.

$3^{\frac{3}{7}} x^{1} = 33^{\frac{3}{7}}$

Step 3.1.3

Simplify.

$3^{\frac{3}{7}} x = 33^{\frac{3}{7}}$

Step 3.1.4

Reorder factors in $3^{\frac{3}{7}} x$ .

$x \cdot 3^{\frac{3}{7}} = 33^{\frac{3}{7}}$

Step 4

Divide each term in $x \cdot 3^{\frac{3}{7}} = 33^{\frac{3}{7}}$ by $3^{\frac{3}{7}}$ and simplify.

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Step 4.1

Divide each term in $x \cdot 3^{\frac{3}{7}} = 33^{\frac{3}{7}}$ by $3^{\frac{3}{7}}$ .

$\frac{x \cdot 3^{\frac{3}{7}}}{3^{\frac{3}{7}}} = \frac{33^{\frac{3}{7}}}{3^{\frac{3}{7}}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor.

$\frac{x \cdot 3^{\frac{3}{7}}}{3^{\frac{3}{7}}} = \frac{33^{\frac{3}{7}}}{3^{\frac{3}{7}}}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{33^{\frac{3}{7}}}{3^{\frac{3}{7}}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

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

$x = {(\frac{33}{3})}^{\frac{3}{7}}$

Step 4.3.2

Divide $33$ by $3$ .

$x = 11^{\frac{3}{7}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 11^{\frac{3}{7}}$

Decimal Form:

$x = 2.79454527 \dots$