Solve for a 1/6(12a)^(1/3)=1

$\frac{1}{6} {(12 a)}^{\frac{1}{3}} = 1$

Step 1

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} \cdot {(12 a)}^{\frac{1}{3}}) = 6 \cdot 1$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $6 (\frac{1}{6} \cdot {(12 a)}^{\frac{1}{3}})$ .

Apply the product rule to $12 a$ .

$6 (\frac{1}{6} \cdot (12^{\frac{1}{3}} a^{\frac{1}{3}})) = 6 \cdot 1$

Multiply $\frac{1}{6} (12^{\frac{1}{3}} a^{\frac{1}{3}})$ .

Combine $12^{\frac{1}{3}}$ and $\frac{1}{6}$ .

$6 (\frac{12^{\frac{1}{3}}}{6} a^{\frac{1}{3}}) = 6 \cdot 1$

Combine $\frac{12^{\frac{1}{3}}}{6}$ and $a^{\frac{1}{3}}$ .

$6 \frac{12^{\frac{1}{3}} a^{\frac{1}{3}}}{6} = 6 \cdot 1$

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{12^{\frac{1}{3}} a^{\frac{1}{3}}}{6} = 6 \cdot 1$

Rewrite the expression.

$12^{\frac{1}{3}} a^{\frac{1}{3}} = 6 \cdot 1$

Simplify the right side.

Multiply $6$ by $1$ .

$12^{\frac{1}{3}} a^{\frac{1}{3}} = 6$

Step 3

Divide each term in $12^{\frac{1}{3}} a^{\frac{1}{3}} = 6$ by $12^{\frac{1}{3}}$ and simplify.

Divide each term in $12^{\frac{1}{3}} a^{\frac{1}{3}} = 6$ by $12^{\frac{1}{3}}$ .

$\frac{12^{\frac{1}{3}} a^{\frac{1}{3}}}{12^{\frac{1}{3}}} = \frac{6}{12^{\frac{1}{3}}}$

Simplify the left side.

Cancel the common factor.

$\frac{12^{\frac{1}{3}} a^{\frac{1}{3}}}{12^{\frac{1}{3}}} = \frac{6}{12^{\frac{1}{3}}}$

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

$a^{\frac{1}{3}} = \frac{6}{12^{\frac{1}{3}}}$

Step 4

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

${(a^{\frac{1}{3}})}^{3} = {(\frac{6}{12^{\frac{1}{3}}})}^{3}$

Step 5

Simplify the exponent.

Simplify the left side.

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

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

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

$a^{\frac{1}{3} \cdot 3} = {(\frac{6}{12^{\frac{1}{3}}})}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$a^{\frac{1}{3} \cdot 3} = {(\frac{6}{12^{\frac{1}{3}}})}^{3}$

Rewrite the expression.

$a^{1} = {(\frac{6}{12^{\frac{1}{3}}})}^{3}$

Simplify.

$a = {(\frac{6}{12^{\frac{1}{3}}})}^{3}$

Simplify the right side.

Simplify ${(\frac{6}{12^{\frac{1}{3}}})}^{3}$ .

Simplify the expression.

Apply the product rule to $\frac{6}{12^{\frac{1}{3}}}$ .

$a = \frac{6^{3}}{{(12^{\frac{1}{3}})}^{3}}$

Raise $6$ to the power of $3$ .

$a = \frac{216}{{(12^{\frac{1}{3}})}^{3}}$

Simplify the denominator.

Multiply the exponents in ${(12^{\frac{1}{3}})}^{3}$ .

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

$a = \frac{216}{12^{\frac{1}{3} \cdot 3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$a = \frac{216}{12^{\frac{1}{3} \cdot 3}}$

Rewrite the expression.

$a = \frac{216}{12^{1}}$

Evaluate the exponent.

$a = \frac{216}{12}$

Divide $216$ by $12$ .

$a = 18$

Solve for a 1/6(12a)^(1/3)=1

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