Solve for d 3=54d^(3/2)

$3 = 54 d^{\frac{3}{2}}$

Step 1

Rewrite the equation as $54 d^{\frac{3}{2}} = 3$ .

$54 d^{\frac{3}{2}} = 3$

Step 2

Divide each term in $54 d^{\frac{3}{2}} = 3$ by $54$ and simplify.

Divide each term in $54 d^{\frac{3}{2}} = 3$ by $54$ .

$\frac{54 d^{\frac{3}{2}}}{54} = \frac{3}{54}$

Simplify the left side.

Cancel the common factor.

$\frac{54 d^{\frac{3}{2}}}{54} = \frac{3}{54}$

Divide $d^{\frac{3}{2}}$ by $1$ .

$d^{\frac{3}{2}} = \frac{3}{54}$

Simplify the right side.

Cancel the common factor of $3$ and $54$ .

Factor $3$ out of $3$ .

$d^{\frac{3}{2}} = \frac{3 (1)}{54}$

Cancel the common factors.

Factor $3$ out of $54$ .

$d^{\frac{3}{2}} = \frac{3 \cdot 1}{3 \cdot 18}$

Cancel the common factor.

$d^{\frac{3}{2}} = \frac{3 \cdot 1}{3 \cdot 18}$

Rewrite the expression.

$d^{\frac{3}{2}} = \frac{1}{18}$

Step 3

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(d^{\frac{3}{2}})}^{\frac{2}{3}} = {(\frac{1}{18})}^{\frac{2}{3}}$

Step 4

Simplify the exponent.

Simplify the left side.

Simplify ${(d^{\frac{3}{2}})}^{\frac{2}{3}}$ .

Multiply the exponents in ${(d^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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

$d^{\frac{3}{2} \cdot \frac{2}{3}} = {(\frac{1}{18})}^{\frac{2}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$d^{\frac{3}{2} \cdot \frac{2}{3}} = {(\frac{1}{18})}^{\frac{2}{3}}$

Rewrite the expression.

$d^{\frac{1}{2} \cdot 2} = {(\frac{1}{18})}^{\frac{2}{3}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$d^{\frac{1}{2} \cdot 2} = {(\frac{1}{18})}^{\frac{2}{3}}$

Rewrite the expression.

$d^{1} = {(\frac{1}{18})}^{\frac{2}{3}}$

Simplify.

$d = {(\frac{1}{18})}^{\frac{2}{3}}$

Simplify the right side.

Simplify ${(\frac{1}{18})}^{\frac{2}{3}}$ .

Apply the product rule to $\frac{1}{18}$ .

$d = \frac{1^{\frac{2}{3}}}{18^{\frac{2}{3}}}$

One to any power is one.

$d = \frac{1}{18^{\frac{2}{3}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$d = \frac{1}{18^{\frac{2}{3}}}$

Decimal Form:

$d = 0.14559674 \dots$

Solve for d 3=54d^(3/2)

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