Solve for x 6(x/4)^(1/2)=42

$6 {(\frac{x}{4})}^{\frac{1}{2}} = 42$

Divide each term in $6 {(\frac{x}{4})}^{\frac{1}{2}} = 42$ by $6$ and simplify.

Divide each term in $6 {(\frac{x}{4})}^{\frac{1}{2}} = 42$ by $6$ .

$\frac{6 {(\frac{x}{4})}^{\frac{1}{2}}}{6} = \frac{42}{6}$

Simplify the left side.

Reduce the expression by cancelling the common factors.

Cancel the common factor.

$\frac{6 {(\frac{x}{4})}^{\frac{1}{2}}}{6} = \frac{42}{6}$

Simplify the expression.

Divide ${(\frac{x}{4})}^{\frac{1}{2}}$ by $1$ .

${(\frac{x}{4})}^{\frac{1}{2}} = \frac{42}{6}$

Apply the product rule to $\frac{x}{4}$ .

$\frac{x^{\frac{1}{2}}}{4^{\frac{1}{2}}} = \frac{42}{6}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{x^{\frac{1}{2}}}{{(2^{2})}^{\frac{1}{2}}} = \frac{42}{6}$

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

$\frac{x^{\frac{1}{2}}}{2^{2 (\frac{1}{2})}} = \frac{42}{6}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x^{\frac{1}{2}}}{2^{2 (\frac{1}{2})}} = \frac{42}{6}$

Rewrite the expression.

$\frac{x^{\frac{1}{2}}}{2^{1}} = \frac{42}{6}$

Evaluate the exponent.

$\frac{x^{\frac{1}{2}}}{2} = \frac{42}{6}$

Simplify the right side.

Divide $42$ by $6$ .

$\frac{x^{\frac{1}{2}}}{2} = 7$

Multiply both sides of the equation by $2$ .

$2 \frac{x^{\frac{1}{2}}}{2} = 2 \cdot 7$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{x^{\frac{1}{2}}}{2} = 2 \cdot 7$

Rewrite the expression.

$x^{\frac{1}{2}} = 2 \cdot 7$

Simplify the right side.

Multiply $2$ by $7$ .

$x^{\frac{1}{2}} = 14$

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{2}})}^{2} = 14^{2}$

Simplify the exponent.

Simplify the left side.

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

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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

$x^{\frac{1}{2} \cdot 2} = 14^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 14^{2}$

Rewrite the expression.

$x^{1} = 14^{2}$

Simplify.

$x = 14^{2}$

Simplify the right side.

Raise $14$ to the power of $2$ .

$x = 196$

Solve for x 6(x/4)^(1/2)=42

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