Basic Math Examples

$12 b^{2} \cdot (7 b) = 3$

Step 1

Simplify.

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Step 1.1

Multiply $7$ by $12$ .

$84 b^{2} \cdot b = 3$

Step 1.2

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

$84 (b^{1} b^{2}) = 3$

Step 1.3

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

$84 b^{1 + 2} = 3$

Step 1.4

Add $1$ and $2$ .

$84 b^{3} = 3$

Step 2

Divide each term in $84 b^{3} = 3$ by $84$ and simplify.

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Step 2.1

Divide each term in $84 b^{3} = 3$ by $84$ .

$\frac{84 b^{3}}{84} = \frac{3}{84}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $84$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{84 b^{3}}{84} = \frac{3}{84}$

Step 2.2.1.2

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

$b^{3} = \frac{3}{84}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $3$ and $84$ .

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Step 2.3.1.1

Factor $3$ out of $3$ .

$b^{3} = \frac{3 (1)}{84}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $3$ out of $84$ .

$b^{3} = \frac{3 \cdot 1}{3 \cdot 28}$

Step 2.3.1.2.2

Cancel the common factor.

$b^{3} = \frac{3 \cdot 1}{3 \cdot 28}$

Step 2.3.1.2.3

Rewrite the expression.

$b^{3} = \frac{1}{28}$

Step 3

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

$b = \sqrt[3]{\frac{1}{28}}$

Step 4

Simplify $\sqrt[3]{\frac{1}{28}}$ .

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Step 4.1

Rewrite $\sqrt[3]{\frac{1}{28}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{28}}$ .

$b = \frac{\sqrt[3]{1}}{\sqrt[3]{28}}$

Step 4.2

Any root of $1$ is $1$ .

$b = \frac{1}{\sqrt[3]{28}}$

Step 4.3

Multiply $\frac{1}{\sqrt[3]{28}}$ by $\frac{{\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{2}}$ .

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

Step 4.4

Combine and simplify the denominator.

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Step 4.4.1

Multiply $\frac{1}{\sqrt[3]{28}}$ by $\frac{{\sqrt[3]{28}}^{2}}{{\sqrt[3]{28}}^{2}}$ .

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

Step 4.4.2

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

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

Step 4.4.3

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

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

Step 4.4.4

Add $1$ and $2$ .

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

Step 4.4.5

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

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Step 4.4.5.1

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

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

Step 4.4.5.2

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

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

Step 4.4.5.3

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

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

Step 4.4.5.4

Cancel the common factor of $3$ .

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Step 4.4.5.4.1

Cancel the common factor.

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

Step 4.4.5.4.2

Rewrite the expression.

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

Step 4.4.5.5

Evaluate the exponent.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

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

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

Step 4.5.2

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

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

Step 4.5.3

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

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Step 4.5.3.1

Factor $8$ out of $784$ .

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

Step 4.5.3.2

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

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

Step 4.5.4

Pull terms out from under the radical.

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

Step 4.6

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

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Step 4.6.1

Factor $2$ out of $2 \sqrt[3]{98}$ .

$b = \frac{2 (\sqrt[3]{98})}{28}$

Step 4.6.2

Cancel the common factors.

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Step 4.6.2.1

Factor $2$ out of $28$ .

$b = \frac{2 \sqrt[3]{98}}{2 \cdot 14}$

Step 4.6.2.2

Cancel the common factor.

$b = \frac{2 \sqrt[3]{98}}{2 \cdot 14}$

Step 4.6.2.3

Rewrite the expression.

$b = \frac{\sqrt[3]{98}}{14}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \frac{\sqrt[3]{98}}{14}$

Decimal Form:

$b = 0.32931687 \dots$