Basic Math Examples

$4 s^{2} \cdot (7 s) - 3 = 0$

Step 1

Simplify each term.

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Step 1.1

Rewrite using the commutative property of multiplication.

$4 \cdot 7 s^{2} s - 3 = 0$

Step 1.2

Multiply $s^{2}$ by $s$ by adding the exponents.

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Step 1.2.1

Move $s$ .

$4 \cdot 7 (s \cdot s^{2}) - 3 = 0$

Step 1.2.2

Multiply $s$ by $s^{2}$ .

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Step 1.2.2.1

Raise $s$ to the power of $1$ .

$4 \cdot 7 (s^{1} s^{2}) - 3 = 0$

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 7 s^{1 + 2} - 3 = 0$

Step 1.2.3

Add $1$ and $2$ .

$4 \cdot 7 s^{3} - 3 = 0$

Step 1.3

Multiply $4$ by $7$ .

$28 s^{3} - 3 = 0$

Step 2

Add $3$ to both sides of the equation.

$28 s^{3} = 3$

Step 3

Divide each term in $28 s^{3} = 3$ by $28$ and simplify.

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Step 3.1

Divide each term in $28 s^{3} = 3$ by $28$ .

$\frac{28 s^{3}}{28} = \frac{3}{28}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $28$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{28 s^{3}}{28} = \frac{3}{28}$

Step 3.2.1.2

Divide $s^{3}$ by $1$ .

$s^{3} = \frac{3}{28}$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$s = \sqrt[3]{\frac{3}{28}}$

Step 5

Simplify $\sqrt[3]{\frac{3}{28}}$ .

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Step 5.1

Rewrite $\sqrt[3]{\frac{3}{28}}$ as $\frac{\sqrt[3]{3}}{\sqrt[3]{28}}$ .

$s = \frac{\sqrt[3]{3}}{\sqrt[3]{28}}$

Step 5.2

Multiply $\frac{\sqrt[3]{3}}{\sqrt[3]{28}}$ by $\frac{{\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{2}}$ .

$s = \frac{\sqrt[3]{3}}{\sqrt[3]{28}} \cdot \frac{{\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{2}}$

Step 5.3

Combine and simplify the denominator.

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Step 5.3.1

Multiply $\frac{\sqrt[3]{3}}{\sqrt[3]{28}}$ by $\frac{{\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{2}}$ .

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{\sqrt[3]{28} {\sqrt[3]{28}}^{2}}$

Step 5.3.2

Raise $\sqrt[3]{28}$ to the power of $1$ .

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{1} {\sqrt[3]{28}}^{2}}$

Step 5.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{1 + 2}}$

Step 5.3.4

Add $1$ and $2$ .

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{3}}$

Step 5.3.5

Rewrite ${\sqrt[3]{28}}^{3}$ as $28$ .

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Step 5.3.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{28}$ as $28^{\frac{1}{3}}$ .

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{{(28^{\frac{1}{3}})}^{3}}$

Step 5.3.5.2

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

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{28^{\frac{1}{3} \cdot 3}}$

Step 5.3.5.3

Combine $\frac{1}{3}$ and $3$ .

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{28^{\frac{3}{3}}}$

Step 5.3.5.4

Cancel the common factor of $3$ .

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Step 5.3.5.4.1

Cancel the common factor.

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{28^{\frac{3}{3}}}$

Step 5.3.5.4.2

Rewrite the expression.

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{28^{1}}$

Step 5.3.5.5

Evaluate the exponent.

$s = \frac{\sqrt[3]{3} {\sqrt[3]{28}}^{2}}{28}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Rewrite ${\sqrt[3]{28}}^{2}$ as $\sqrt[3]{28^{2}}$ .

$s = \frac{\sqrt[3]{3} \sqrt[3]{28^{2}}}{28}$

Step 5.4.2

Raise $28$ to the power of $2$ .

$s = \frac{\sqrt[3]{3} \sqrt[3]{784}}{28}$

Step 5.4.3

Rewrite $784$ as $2^{3} \cdot 98$ .

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Step 5.4.3.1

Factor $8$ out of $784$ .

$s = \frac{\sqrt[3]{3} \sqrt[3]{8 (98)}}{28}$

Step 5.4.3.2

Rewrite $8$ as $2^{3}$ .

$s = \frac{\sqrt[3]{3} \sqrt[3]{2^{3} \cdot 98}}{28}$

Step 5.4.4

Pull terms out from under the radical.

$s = \frac{\sqrt[3]{3} \cdot 2 \sqrt[3]{98}}{28}$

Step 5.4.5

Combine exponents.

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Step 5.4.5.1

Combine using the product rule for radicals.

$s = \frac{2 \sqrt[3]{3 \cdot 98}}{28}$

Step 5.4.5.2

Multiply $3$ by $98$ .

$s = \frac{2 \sqrt[3]{294}}{28}$

Step 5.5

Cancel the common factor of $2$ and $28$ .

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Step 5.5.1

Factor $2$ out of $2 \sqrt[3]{294}$ .

$s = \frac{2 (\sqrt[3]{294})}{28}$

Step 5.5.2

Cancel the common factors.

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Step 5.5.2.1

Factor $2$ out of $28$ .

$s = \frac{2 \sqrt[3]{294}}{2 \cdot 14}$

Step 5.5.2.2

Cancel the common factor.

$s = \frac{2 \sqrt[3]{294}}{2 \cdot 14}$

Step 5.5.2.3

Rewrite the expression.

$s = \frac{\sqrt[3]{294}}{14}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$s = \frac{\sqrt[3]{294}}{14}$

Decimal Form:

$s = 0.47495712 \dots$