Basic Math Examples

$16 s^{2} \cdot (40 s) = - 25$

Step 1

Simplify.

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Step 1.1

Multiply $40$ by $16$ .

$640 s^{2} \cdot s = - 25$

Step 1.2

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

$640 (s^{1} s^{2}) = - 25$

Step 1.3

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

$640 s^{1 + 2} = - 25$

Step 1.4

Add $1$ and $2$ .

$640 s^{3} = - 25$

Step 2

Divide each term in $640 s^{3} = - 25$ by $640$ and simplify.

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Step 2.1

Divide each term in $640 s^{3} = - 25$ by $640$ .

$\frac{640 s^{3}}{640} = \frac{- 25}{640}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $640$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{640 s^{3}}{640} = \frac{- 25}{640}$

Step 2.2.1.2

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

$s^{3} = \frac{- 25}{640}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $- 25$ and $640$ .

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Step 2.3.1.1

Factor $5$ out of $- 25$ .

$s^{3} = \frac{5 (- 5)}{640}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $5$ out of $640$ .

$s^{3} = \frac{5 \cdot - 5}{5 \cdot 128}$

Step 2.3.1.2.2

Cancel the common factor.

$s^{3} = \frac{5 \cdot - 5}{5 \cdot 128}$

Step 2.3.1.2.3

Rewrite the expression.

$s^{3} = \frac{- 5}{128}$

Step 2.3.2

Move the negative in front of the fraction.

$s^{3} = - \frac{5}{128}$

Step 3

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

$s = \sqrt[3]{- \frac{5}{128}}$

Step 4

Simplify $\sqrt[3]{- \frac{5}{128}}$ .

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Step 4.1

Rewrite $- \frac{5}{128}$ as ${(- \frac{1}{4})}^{3} \frac{5}{2}$ .

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Step 4.1.1

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$s = \sqrt[3]{{(- 1)}^{3} \frac{5}{128}}$

Step 4.1.2

Factor the perfect power $1^{3}$ out of $5$ .

$s = \sqrt[3]{{(- 1)}^{3} \frac{1^{3} \cdot 5}{128}}$

Step 4.1.3

Factor the perfect power $4^{3}$ out of $128$ .

$s = \sqrt[3]{{(- 1)}^{3} \frac{1^{3} \cdot 5}{4^{3} \cdot 2}}$

Step 4.1.4

Rearrange the fraction $\frac{1^{3} \cdot 5}{4^{3} \cdot 2}$ .

$s = \sqrt[3]{{(- 1)}^{3} ({(\frac{1}{4})}^{3} \frac{5}{2})}$

Step 4.1.5

Rewrite ${(- 1)}^{3} {(\frac{1}{4})}^{3}$ as ${(- \frac{1}{4})}^{3}$ .

$s = \sqrt[3]{{(- \frac{1}{4})}^{3} \frac{5}{2}}$

Step 4.2

Pull terms out from under the radical.

$s = - \frac{1}{4} \sqrt[3]{\frac{5}{2}}$

Step 4.3

Rewrite $\sqrt[3]{\frac{5}{2}}$ as $\frac{\sqrt[3]{5}}{\sqrt[3]{2}}$ .

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5}}{\sqrt[3]{2}}$

Step 4.4

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

$s = - \frac{1}{4} (\frac{\sqrt[3]{5}}{\sqrt[3]{2}} \cdot \frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}})$

Step 4.5

Combine and simplify the denominator.

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Step 4.5.1

Multiply $\frac{\sqrt[3]{5}}{\sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{\sqrt[3]{2} {\sqrt[3]{2}}^{2}}$

Step 4.5.2

Raise $\sqrt[3]{2}$ to the power of $1$ .

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{1} {\sqrt[3]{2}}^{2}}$

Step 4.5.3

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

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{1 + 2}}$

Step 4.5.4

Add $1$ and $2$ .

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{3}}$

Step 4.5.5

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

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Step 4.5.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{{(2^{\frac{1}{3}})}^{3}}$

Step 4.5.5.2

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

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{\frac{1}{3} \cdot 3}}$

Step 4.5.5.3

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

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{\frac{3}{3}}}$

Step 4.5.5.4

Cancel the common factor of $3$ .

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Step 4.5.5.4.1

Cancel the common factor.

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{\frac{3}{3}}}$

Step 4.5.5.4.2

Rewrite the expression.

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2^{1}}$

Step 4.5.5.5

Evaluate the exponent.

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} {\sqrt[3]{2}}^{2}}{2}$

Step 4.6

Simplify the numerator.

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Step 4.6.1

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

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} \sqrt[3]{2^{2}}}{2}$

Step 4.6.2

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

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5} \sqrt[3]{4}}{2}$

Step 4.7

Simplify the numerator.

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Step 4.7.1

Combine using the product rule for radicals.

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{5 \cdot 4}}{2}$

Step 4.7.2

Multiply $5$ by $4$ .

$s = - \frac{1}{4} \cdot \frac{\sqrt[3]{20}}{2}$

Step 4.8

Multiply $- \frac{1}{4} \cdot \frac{\sqrt[3]{20}}{2}$ .

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Step 4.8.1

Multiply $\frac{\sqrt[3]{20}}{2}$ by $\frac{1}{4}$ .

$s = - \frac{\sqrt[3]{20}}{2 \cdot 4}$

Step 4.8.2

Multiply $2$ by $4$ .

$s = - \frac{\sqrt[3]{20}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$s = - \frac{\sqrt[3]{20}}{8}$

Decimal Form:

$s = - 0.33930220 \dots$