Algebra Examples

$3 - \sqrt[4]{9 d} = 0$

Step 1

Subtract $3$ from both sides of the equation.

$- \sqrt[4]{9 d} = - 3$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${(- \sqrt[4]{9 d})}^{4} = {(- 3)}^{4}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{9 d}$ as ${(9 d)}^{\frac{1}{4}}$ .

${(- {(9 d)}^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(- {(9 d)}^{\frac{1}{4}})}^{4}$ .

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Step 3.2.1.1

Apply the product rule to $9 d$ .

${(- (9^{\frac{1}{4}} d^{\frac{1}{4}}))}^{4} = {(- 3)}^{4}$

Step 3.2.1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.2.1.2.1

Apply the product rule to $- 9^{\frac{1}{4}} d^{\frac{1}{4}}$ .

${(- 9^{\frac{1}{4}})}^{4} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.2.2

Apply the product rule to $- 9^{\frac{1}{4}}$ .

${(- 1)}^{4} {(9^{\frac{1}{4}})}^{4} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.3

Raise $- 1$ to the power of $4$ .

$1 {(9^{\frac{1}{4}})}^{4} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.4

Multiply ${(9^{\frac{1}{4}})}^{4}$ by $1$ .

${(9^{\frac{1}{4}})}^{4} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.5

Multiply the exponents in ${(9^{\frac{1}{4}})}^{4}$ .

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Step 3.2.1.5.1

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

$9^{\frac{1}{4} \cdot 4} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.5.2

Cancel the common factor of $4$ .

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Step 3.2.1.5.2.1

Cancel the common factor.

$9^{\frac{1}{4} \cdot 4} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.5.2.2

Rewrite the expression.

$9^{1} {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.6

Evaluate the exponent.

$9 {(d^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2.1.7

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

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Step 3.2.1.7.1

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

$9 d^{\frac{1}{4} \cdot 4} = {(- 3)}^{4}$

Step 3.2.1.7.2

Cancel the common factor of $4$ .

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Step 3.2.1.7.2.1

Cancel the common factor.

$9 d^{\frac{1}{4} \cdot 4} = {(- 3)}^{4}$

Step 3.2.1.7.2.2

Rewrite the expression.

$9 d^{1} = {(- 3)}^{4}$

Step 3.2.1.8

Simplify.

$9 d = {(- 3)}^{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$9 d = 81$

Step 4

Divide each term in $9 d = 81$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 d = 81$ by $9$ .

$\frac{9 d}{9} = \frac{81}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 d}{9} = \frac{81}{9}$

Step 4.2.1.2

Divide $d$ by $1$ .

$d = \frac{81}{9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $81$ by $9$ .

$d = 9$