Basic Math Examples

$1.89 = \frac{13.5}{{(\frac{d}{64})}^{\frac{1}{3}}}$

Step 1

Rewrite the equation as $\frac{13.5}{{(\frac{d}{64})}^{\frac{1}{3}}} = 1.89$ .

$\frac{13.5}{{(\frac{d}{64})}^{\frac{1}{3}}} = 1.89$

Step 2

Factor each term.

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Step 2.1

Simplify the denominator.

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Step 2.1.1

Apply the product rule to $\frac{d}{64}$ .

$\frac{13.5}{\frac{d^{\frac{1}{3}}}{64^{\frac{1}{3}}}} = 1.89$

Step 2.1.2

Simplify the denominator.

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Step 2.1.2.1

Rewrite $64$ as $4^{3}$ .

$\frac{13.5}{\frac{d^{\frac{1}{3}}}{{(4^{3})}^{\frac{1}{3}}}} = 1.89$

Step 2.1.2.2

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

$\frac{13.5}{\frac{d^{\frac{1}{3}}}{4^{3 (\frac{1}{3})}}} = 1.89$

Step 2.1.2.3

Cancel the common factor of $3$ .

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Step 2.1.2.3.1

Cancel the common factor.

$\frac{13.5}{\frac{d^{\frac{1}{3}}}{4^{3 (\frac{1}{3})}}} = 1.89$

Step 2.1.2.3.2

Rewrite the expression.

$\frac{13.5}{\frac{d^{\frac{1}{3}}}{4^{1}}} = 1.89$

Step 2.1.2.4

Evaluate the exponent.

$\frac{13.5}{\frac{d^{\frac{1}{3}}}{4}} = 1.89$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$13.5 \frac{4}{d^{\frac{1}{3}}} = 1.89$

Step 2.3

Multiply $13.5 \frac{4}{d^{\frac{1}{3}}}$ .

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Step 2.3.1

Combine $13.5$ and $\frac{4}{d^{\frac{1}{3}}}$ .

$\frac{13.5 \cdot 4}{d^{\frac{1}{3}}} = 1.89$

Step 2.3.2

Multiply $13.5$ by $4$ .

$\frac{54}{d^{\frac{1}{3}}} = 1.89$

Step 3

Find the LCD of the terms in the equation.

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Step 3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$d^{\frac{1}{3}}, 1$

Step 3.2

The LCM of one and any expression is the expression.

$d^{\frac{1}{3}}$

Step 4

Multiply each term in $\frac{54}{d^{\frac{1}{3}}} = 1.89$ by $d^{\frac{1}{3}}$ to eliminate the fractions.

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Step 4.1

Multiply each term in $\frac{54}{d^{\frac{1}{3}}} = 1.89$ by $d^{\frac{1}{3}}$ .

$\frac{54}{d^{\frac{1}{3}}} d^{\frac{1}{3}} = 1.89 d^{\frac{1}{3}}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $d^{\frac{1}{3}}$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{54}{d^{\frac{1}{3}}} d^{\frac{1}{3}} = 1.89 d^{\frac{1}{3}}$

Step 4.2.1.2

Rewrite the expression.

$54 = 1.89 d^{\frac{1}{3}}$

Step 5

Solve the equation.

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Step 5.1

Rewrite the equation as $1.89 d^{\frac{1}{3}} = 54$ .

$1.89 d^{\frac{1}{3}} = 54$

Step 5.2

Divide each term in $1.89 d^{\frac{1}{3}} = 54$ by $1.89$ and simplify.

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Step 5.2.1

Divide each term in $1.89 d^{\frac{1}{3}} = 54$ by $1.89$ .

$\frac{1.89 d^{\frac{1}{3}}}{1.89} = \frac{54}{1.89}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor.

$\frac{1.89 d^{\frac{1}{3}}}{1.89} = \frac{54}{1.89}$

Step 5.2.2.2

Divide $d^{\frac{1}{3}}$ by $1$ .

$d^{\frac{1}{3}} = \frac{54}{1.89}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $54$ by $1.89$ .

$d^{\frac{1}{3}} = 28.\overline{571428}$

Step 5.3

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(d^{\frac{1}{3}})}^{3} = {28.\overline{571428}}^{3}$

Step 5.4

Simplify the exponent.

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Step 5.4.1

Simplify the left side.

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Step 5.4.1.1

Simplify ${(d^{\frac{1}{3}})}^{3}$ .

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Step 5.4.1.1.1

Multiply the exponents in ${(d^{\frac{1}{3}})}^{3}$ .

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Step 5.4.1.1.1.1

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

$d^{\frac{1}{3} \cdot 3} = {28.\overline{571428}}^{3}$

Step 5.4.1.1.1.2

Cancel the common factor of $3$ .

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Step 5.4.1.1.1.2.1

Cancel the common factor.

$d^{\frac{1}{3} \cdot 3} = {28.\overline{571428}}^{3}$

Step 5.4.1.1.1.2.2

Rewrite the expression.

$d^{1} = {28.\overline{571428}}^{3}$

Step 5.4.1.1.2

Simplify.

$d = {28.\overline{571428}}^{3}$

Step 5.4.2

Simplify the right side.

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Step 5.4.2.1

Raise $28.\overline{571428}$ to the power of $3$ .

$d = 23323.61516034$