Solve for t 3(4-t)^(1/4)=6^(1/4)

$3 {(4 - t)}^{\frac{1}{4}} = 6^{\frac{1}{4}}$

Step 1

Divide each term in $3 {(4 - t)}^{\frac{1}{4}} = 6^{\frac{1}{4}}$ by $3$ and simplify.

Divide each term in $3 {(4 - t)}^{\frac{1}{4}} = 6^{\frac{1}{4}}$ by $3$ .

$\frac{3 {(4 - t)}^{\frac{1}{4}}}{3} = \frac{6^{\frac{1}{4}}}{3}$

Simplify the left side.

Cancel the common factor.

$\frac{3 {(4 - t)}^{\frac{1}{4}}}{3} = \frac{6^{\frac{1}{4}}}{3}$

Divide ${(4 - t)}^{\frac{1}{4}}$ by $1$ .

${(4 - t)}^{\frac{1}{4}} = \frac{6^{\frac{1}{4}}}{3}$

Step 2

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

${({(4 - t)}^{\frac{1}{4}})}^{4} = {(\frac{6^{\frac{1}{4}}}{3})}^{4}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${({(4 - t)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(4 - t)}^{\frac{1}{4}})}^{4}$ .

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

${(4 - t)}^{\frac{1}{4} \cdot 4} = {(\frac{6^{\frac{1}{4}}}{3})}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(4 - t)}^{\frac{1}{4} \cdot 4} = {(\frac{6^{\frac{1}{4}}}{3})}^{4}$

Rewrite the expression.

${(4 - t)}^{1} = {(\frac{6^{\frac{1}{4}}}{3})}^{4}$

Simplify.

$4 - t = {(\frac{6^{\frac{1}{4}}}{3})}^{4}$

Simplify the right side.

Simplify ${(\frac{6^{\frac{1}{4}}}{3})}^{4}$ .

Apply the product rule to $\frac{6^{\frac{1}{4}}}{3}$ .

$4 - t = \frac{{(6^{\frac{1}{4}})}^{4}}{3^{4}}$

Simplify the numerator.

Multiply the exponents in ${(6^{\frac{1}{4}})}^{4}$ .

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

$4 - t = \frac{6^{\frac{1}{4} \cdot 4}}{3^{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 - t = \frac{6^{\frac{1}{4} \cdot 4}}{3^{4}}$

Rewrite the expression.

$4 - t = \frac{6^{1}}{3^{4}}$

Evaluate the exponent.

$4 - t = \frac{6}{3^{4}}$

Reduce the expression by cancelling the common factors.

Raise $3$ to the power of $4$ .

$4 - t = \frac{6}{81}$

Cancel the common factor of $6$ and $81$ .

Factor $3$ out of $6$ .

$4 - t = \frac{3 (2)}{81}$

Cancel the common factors.

Factor $3$ out of $81$ .

$4 - t = \frac{3 \cdot 2}{3 \cdot 27}$

Cancel the common factor.

$4 - t = \frac{3 \cdot 2}{3 \cdot 27}$

Rewrite the expression.

$4 - t = \frac{2}{27}$

Step 4

Solve for $t$ .

Move all terms not containing $t$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$- t = \frac{2}{27} - 4$

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$- t = \frac{2}{27} - 4 \cdot \frac{27}{27}$

Combine $- 4$ and $\frac{27}{27}$ .

$- t = \frac{2}{27} + \frac{- 4 \cdot 27}{27}$

Combine the numerators over the common denominator.

$- t = \frac{2 - 4 \cdot 27}{27}$

Simplify the numerator.

Multiply $- 4$ by $27$ .

$- t = \frac{2 - 108}{27}$

Subtract $108$ from $2$ .

$- t = \frac{- 106}{27}$

Move the negative in front of the fraction.

$- t = - \frac{106}{27}$

Divide each term in $- t = - \frac{106}{27}$ by $- 1$ and simplify.

Divide each term in $- t = - \frac{106}{27}$ by $- 1$ .

$\frac{- t}{- 1} = \frac{- \frac{106}{27}}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{t}{1} = \frac{- \frac{106}{27}}{- 1}$

Divide $t$ by $1$ .

$t = \frac{- \frac{106}{27}}{- 1}$

Simplify the right side.

Dividing two negative values results in a positive value.

$t = \frac{\frac{106}{27}}{1}$

Divide $\frac{106}{27}$ by $1$ .

$t = \frac{106}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$t = \frac{106}{27}$

Decimal Form:

$t = 3.\overline{925}$

Mixed Number Form:

$t = 3 \frac{25}{27}$

Solve for t 3(4-t)^(1/4)=6^(1/4)

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