Finite Math Examples

$7 x^{\frac{5}{3}} - 21 = 0$

Step 1

Add $21$ to both sides of the equation.

$7 x^{\frac{5}{3}} = 21$

Step 2

Raise each side of the equation to the power of $\frac{3}{5}$ to eliminate the fractional exponent on the left side.

${(7 x^{\frac{5}{3}})}^{\frac{3}{5}} = 21^{\frac{3}{5}}$

Step 3

Simplify the left side.

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Step 3.1

Simplify ${(7 x^{\frac{5}{3}})}^{\frac{3}{5}}$ .

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Step 3.1.1

Apply the product rule to $7 x^{\frac{5}{3}}$ .

$7^{\frac{3}{5}} {(x^{\frac{5}{3}})}^{\frac{3}{5}} = 21^{\frac{3}{5}}$

Step 3.1.2

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

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Step 3.1.2.1

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

$7^{\frac{3}{5}} x^{\frac{5}{3} \cdot \frac{3}{5}} = 21^{\frac{3}{5}}$

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.

$7^{\frac{3}{5}} x^{\frac{5}{3} \cdot \frac{3}{5}} = 21^{\frac{3}{5}}$

Step 3.1.2.2.2

Rewrite the expression.

$7^{\frac{3}{5}} x^{\frac{1}{3} \cdot 3} = 21^{\frac{3}{5}}$

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.

$7^{\frac{3}{5}} x^{\frac{1}{3} \cdot 3} = 21^{\frac{3}{5}}$

Step 3.1.2.3.2

Rewrite the expression.

$7^{\frac{3}{5}} x^{1} = 21^{\frac{3}{5}}$

Step 3.1.3

Simplify.

$7^{\frac{3}{5}} x = 21^{\frac{3}{5}}$

Step 3.1.4

Reorder factors in $7^{\frac{3}{5}} x$ .

$x \cdot 7^{\frac{3}{5}} = 21^{\frac{3}{5}}$

Step 4

Divide each term in $x \cdot 7^{\frac{3}{5}} = 21^{\frac{3}{5}}$ by $7^{\frac{3}{5}}$ and simplify.

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Step 4.1

Divide each term in $x \cdot 7^{\frac{3}{5}} = 21^{\frac{3}{5}}$ by $7^{\frac{3}{5}}$ .

$\frac{x \cdot 7^{\frac{3}{5}}}{7^{\frac{3}{5}}} = \frac{21^{\frac{3}{5}}}{7^{\frac{3}{5}}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor.

$\frac{x \cdot 7^{\frac{3}{5}}}{7^{\frac{3}{5}}} = \frac{21^{\frac{3}{5}}}{7^{\frac{3}{5}}}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{21^{\frac{3}{5}}}{7^{\frac{3}{5}}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

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

$x = {(\frac{21}{7})}^{\frac{3}{5}}$

Step 4.3.2

Divide $21$ by $7$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.93318204 \dots$