Algebra Examples

$3 = (5^{\frac{1}{3}}) (x^{\frac{1}{3}})$

Step 1

Rewrite the equation as $5^{\frac{1}{3}} x^{\frac{1}{3}} = 3$ .

$5^{\frac{1}{3}} x^{\frac{1}{3}} = 3$

Step 2

Divide each term in $5^{\frac{1}{3}} x^{\frac{1}{3}} = 3$ by $5^{\frac{1}{3}}$ and simplify.

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Step 2.1

Divide each term in $5^{\frac{1}{3}} x^{\frac{1}{3}} = 3$ by $5^{\frac{1}{3}}$ .

$\frac{5^{\frac{1}{3}} x^{\frac{1}{3}}}{5^{\frac{1}{3}}} = \frac{3}{5^{\frac{1}{3}}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor.

$\frac{5^{\frac{1}{3}} x^{\frac{1}{3}}}{5^{\frac{1}{3}}} = \frac{3}{5^{\frac{1}{3}}}$

Step 2.2.2

Divide $x^{\frac{1}{3}}$ by $1$ .

$x^{\frac{1}{3}} = \frac{3}{5^{\frac{1}{3}}}$

Step 3

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{3}})}^{3} = {(\frac{3}{5^{\frac{1}{3}}})}^{3}$

Step 4

Simplify the exponent.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify ${(x^{\frac{1}{3}})}^{3}$ .

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Step 4.1.1.1

Multiply the exponents in ${(x^{\frac{1}{3}})}^{3}$ .

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Step 4.1.1.1.1

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

$x^{\frac{1}{3} \cdot 3} = {(\frac{3}{5^{\frac{1}{3}}})}^{3}$

Step 4.1.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = {(\frac{3}{5^{\frac{1}{3}}})}^{3}$

Step 4.1.1.1.2.2

Rewrite the expression.

$x^{1} = {(\frac{3}{5^{\frac{1}{3}}})}^{3}$

Step 4.1.1.2

Simplify.

$x = {(\frac{3}{5^{\frac{1}{3}}})}^{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify ${(\frac{3}{5^{\frac{1}{3}}})}^{3}$ .

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Step 4.2.1.1

Simplify the expression.

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Step 4.2.1.1.1

Apply the product rule to $\frac{3}{5^{\frac{1}{3}}}$ .

$x = \frac{3^{3}}{{(5^{\frac{1}{3}})}^{3}}$

Step 4.2.1.1.2

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

$x = \frac{27}{{(5^{\frac{1}{3}})}^{3}}$

Step 4.2.1.2

Simplify the denominator.

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Step 4.2.1.2.1

Multiply the exponents in ${(5^{\frac{1}{3}})}^{3}$ .

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Step 4.2.1.2.1.1

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

$x = \frac{27}{5^{\frac{1}{3} \cdot 3}}$

Step 4.2.1.2.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.2.1.2.1

Cancel the common factor.

$x = \frac{27}{5^{\frac{1}{3} \cdot 3}}$

Step 4.2.1.2.1.2.2

Rewrite the expression.

$x = \frac{27}{5^{1}}$

Step 4.2.1.2.2

Evaluate the exponent.

$x = \frac{27}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{27}{5}$

Decimal Form:

$x = 5.4$

Mixed Number Form:

$x = 5 \frac{2}{5}$