Pre-Algebra Examples

$5 x^{\frac{7}{2}} - 15 = 0$

Step 1

Add $15$ to both sides of the equation.

$5 x^{\frac{7}{2}} = 15$

Step 2

Raise each side of the equation to the power of $\frac{2}{7}$ to eliminate the fractional exponent on the left side.

${(5 x^{\frac{7}{2}})}^{\frac{2}{7}} = 15^{\frac{2}{7}}$

Step 3

Simplify the left side.

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Step 3.1

Simplify ${(5 x^{\frac{7}{2}})}^{\frac{2}{7}}$ .

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Step 3.1.1

Apply the product rule to $5 x^{\frac{7}{2}}$ .

$5^{\frac{2}{7}} {(x^{\frac{7}{2}})}^{\frac{2}{7}} = 15^{\frac{2}{7}}$

Step 3.1.2

Multiply the exponents in ${(x^{\frac{7}{2}})}^{\frac{2}{7}}$ .

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Step 3.1.2.1

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

$5^{\frac{2}{7}} x^{\frac{7}{2} \cdot \frac{2}{7}} = 15^{\frac{2}{7}}$

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.

$5^{\frac{2}{7}} x^{\frac{7}{2} \cdot \frac{2}{7}} = 15^{\frac{2}{7}}$

Step 3.1.2.2.2

Rewrite the expression.

$5^{\frac{2}{7}} x^{\frac{1}{2} \cdot 2} = 15^{\frac{2}{7}}$

Step 3.1.2.3

Cancel the common factor of $2$ .

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Step 3.1.2.3.1

Cancel the common factor.

$5^{\frac{2}{7}} x^{\frac{1}{2} \cdot 2} = 15^{\frac{2}{7}}$

Step 3.1.2.3.2

Rewrite the expression.

$5^{\frac{2}{7}} x^{1} = 15^{\frac{2}{7}}$

Step 3.1.3

Simplify.

$5^{\frac{2}{7}} x = 15^{\frac{2}{7}}$

Step 3.1.4

Reorder factors in $5^{\frac{2}{7}} x$ .

$x \cdot 5^{\frac{2}{7}} = 15^{\frac{2}{7}}$

Step 4

Divide each term in $x \cdot 5^{\frac{2}{7}} = 15^{\frac{2}{7}}$ by $5^{\frac{2}{7}}$ and simplify.

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Step 4.1

Divide each term in $x \cdot 5^{\frac{2}{7}} = 15^{\frac{2}{7}}$ by $5^{\frac{2}{7}}$ .

$\frac{x \cdot 5^{\frac{2}{7}}}{5^{\frac{2}{7}}} = \frac{15^{\frac{2}{7}}}{5^{\frac{2}{7}}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor.

$\frac{x \cdot 5^{\frac{2}{7}}}{5^{\frac{2}{7}}} = \frac{15^{\frac{2}{7}}}{5^{\frac{2}{7}}}$

Step 4.2.2

Divide $x$ by $1$ .

$x = \frac{15^{\frac{2}{7}}}{5^{\frac{2}{7}}}$

Step 4.3

Simplify the right side.

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Step 4.3.1

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

$x = {(\frac{15}{5})}^{\frac{2}{7}}$

Step 4.3.2

Divide $15$ by $5$ .

$x = 3^{\frac{2}{7}}$