Pre-Algebra Examples

$0.189 = 4 d^{- \frac{1}{3}} (13.5)$

Step 1

Rewrite the equation as $4 d^{- \frac{1}{3}} \cdot 13.5 = 0.189$ .

$4 d^{- \frac{1}{3}} \cdot 13.5 = 0.189$

Step 2

Multiply $13.5$ by $4$ .

$54 d^{- \frac{1}{3}} = 0.189$

Step 3

Divide each term in $54 d^{- \frac{1}{3}} = 0.189$ by $54$ and simplify.

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Step 3.1

Divide each term in $54 d^{- \frac{1}{3}} = 0.189$ by $54$ .

$\frac{54 d^{- \frac{1}{3}}}{54} = \frac{0.189}{54}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Move $d^{- \frac{1}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{54}{54 d^{\frac{1}{3}}} = \frac{0.189}{54}$

Step 3.2.2

Cancel the common factor.

$\frac{54}{54 d^{\frac{1}{3}}} = \frac{0.189}{54}$

Step 3.2.3

Rewrite the expression.

$\frac{1}{d^{\frac{1}{3}}} = \frac{0.189}{54}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $0.189$ by $54$ .

$\frac{1}{d^{\frac{1}{3}}} = 0.0035$

Step 4

Find the LCD of the terms in the equation.

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Step 4.1

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 4.2

The LCM of one and any expression is the expression.

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

Step 5

Multiply each term in $\frac{1}{d^{\frac{1}{3}}} = 0.0035$ by $d^{\frac{1}{3}}$ to eliminate the fractions.

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Step 5.1

Multiply each term in $\frac{1}{d^{\frac{1}{3}}} = 0.0035$ by $d^{\frac{1}{3}}$ .

$\frac{1}{d^{\frac{1}{3}}} d^{\frac{1}{3}} = 0.0035 d^{\frac{1}{3}}$

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

Cancel the common factor.

$\frac{1}{d^{\frac{1}{3}}} d^{\frac{1}{3}} = 0.0035 d^{\frac{1}{3}}$

Step 5.2.1.2

Rewrite the expression.

$1 = 0.0035 d^{\frac{1}{3}}$

Step 6

Solve the equation.

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Step 6.1

Rewrite the equation as $0.0035 d^{\frac{1}{3}} = 1$ .

$0.0035 d^{\frac{1}{3}} = 1$

Step 6.2

Divide each term in $0.0035 d^{\frac{1}{3}} = 1$ by $0.0035$ and simplify.

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Step 6.2.1

Divide each term in $0.0035 d^{\frac{1}{3}} = 1$ by $0.0035$ .

$\frac{0.0035 d^{\frac{1}{3}}}{0.0035} = \frac{1}{0.0035}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor.

$\frac{0.0035 d^{\frac{1}{3}}}{0.0035} = \frac{1}{0.0035}$

Step 6.2.2.2

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

$d^{\frac{1}{3}} = \frac{1}{0.0035}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $1$ by $0.0035$ .

$d^{\frac{1}{3}} = 285.\overline{714285}$

Step 6.3

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

${(d^{\frac{1}{3}})}^{3} = {285.\overline{714285}}^{3}$

Step 6.4

Simplify the exponent.

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Step 6.4.1

Simplify the left side.

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Step 6.4.1.1

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

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Step 6.4.1.1.1

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

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Step 6.4.1.1.1.1

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

$d^{\frac{1}{3} \cdot 3} = {285.\overline{714285}}^{3}$

Step 6.4.1.1.1.2

Cancel the common factor of $3$ .

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Step 6.4.1.1.1.2.1

Cancel the common factor.

$d^{\frac{1}{3} \cdot 3} = {285.\overline{714285}}^{3}$

Step 6.4.1.1.1.2.2

Rewrite the expression.

$d^{1} = {285.\overline{714285}}^{3}$

Step 6.4.1.1.2

Simplify.

$d = {285.\overline{714285}}^{3}$

Step 6.4.2

Simplify the right side.

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Step 6.4.2.1

Raise $285.\overline{714285}$ to the power of $3$ .

$d = 23323615.1603498$