Solve for d 1.89=4d^(-1/3)*13.5

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

Step 1

Rewrite the equation as $4 d^{- \frac{1}{3}} \cdot 13.5 = 1.89$ .

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

Step 2

Multiply $13.5$ by $4$ .

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

Step 3

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

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

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

Simplify the left side.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Divide $1.89$ by $54$ .

$\frac{1}{d^{\frac{1}{3}}} = 0.035$

Step 4

Find the LCD of the terms in the equation.

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

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

The LCM of one and any expression is the expression.

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

Step 5

Multiply each term in $\frac{1}{d^{\frac{1}{3}}} = 0.035$ by $d^{\frac{1}{3}}$ to eliminate the fractions.

Multiply each term in $\frac{1}{d^{\frac{1}{3}}} = 0.035$ by $d^{\frac{1}{3}}$ .

$\frac{1}{d^{\frac{1}{3}}} d^{\frac{1}{3}} = 0.035 d^{\frac{1}{3}}$

Simplify the left side.

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

Cancel the common factor.

$\frac{1}{d^{\frac{1}{3}}} d^{\frac{1}{3}} = 0.035 d^{\frac{1}{3}}$

Rewrite the expression.

$1 = 0.035 d^{\frac{1}{3}}$

Step 6

Solve the equation.

Rewrite the equation as $0.035 d^{\frac{1}{3}} = 1$ .

$0.035 d^{\frac{1}{3}} = 1$

Divide each term in $0.035 d^{\frac{1}{3}} = 1$ by $0.035$ and simplify.

Divide each term in $0.035 d^{\frac{1}{3}} = 1$ by $0.035$ .

$\frac{0.035 d^{\frac{1}{3}}}{0.035} = \frac{1}{0.035}$

Simplify the left side.

Cancel the common factor.

$\frac{0.035 d^{\frac{1}{3}}}{0.035} = \frac{1}{0.035}$

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

$d^{\frac{1}{3}} = \frac{1}{0.035}$

Simplify the right side.

Divide $1$ by $0.035$ .

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

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

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

Simplify the exponent.

Simplify the left side.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$d = 23323.61516034$

Solve for d 1.89=4d^(-1/3)*13.5

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