Basic Math Examples

${(d - 3)}^{\frac{2}{5}} = 30$

Step 1

Raise each side of the equation to the power of $\frac{5}{2}$ to eliminate the fractional exponent on the left side.

${({(d - 3)}^{\frac{2}{5}})}^{\frac{5}{2}} = \pm 30^{\frac{5}{2}}$

Step 2

Simplify the left side.

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Step 2.1

Simplify ${({(d - 3)}^{\frac{2}{5}})}^{\frac{5}{2}}$ .

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Step 2.1.1

Multiply the exponents in ${({(d - 3)}^{\frac{2}{5}})}^{\frac{5}{2}}$ .

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Step 2.1.1.1

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

${(d - 3)}^{\frac{2}{5} \cdot \frac{5}{2}} = \pm 30^{\frac{5}{2}}$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

${(d - 3)}^{\frac{2}{5} \cdot \frac{5}{2}} = \pm 30^{\frac{5}{2}}$

Step 2.1.1.2.2

Rewrite the expression.

${(d - 3)}^{\frac{1}{5} \cdot 5} = \pm 30^{\frac{5}{2}}$

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Cancel the common factor.

${(d - 3)}^{\frac{1}{5} \cdot 5} = \pm 30^{\frac{5}{2}}$

Step 2.1.1.3.2

Rewrite the expression.

${(d - 3)}^{1} = \pm 30^{\frac{5}{2}}$

Step 2.1.2

Simplify.

$d - 3 = \pm 30^{\frac{5}{2}}$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$d - 3 = 30^{\frac{5}{2}}$

Step 3.2

Add $3$ to both sides of the equation.

$d = 30^{\frac{5}{2}} + 3$

Step 3.3

Next, use the negative value of the $\pm$ to find the second solution.

$d - 3 = - 30^{\frac{5}{2}}$

Step 3.4

Add $3$ to both sides of the equation.

$d = - 30^{\frac{5}{2}} + 3$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

$d = 30^{\frac{5}{2}} + 3, - 30^{\frac{5}{2}} + 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$d = 30^{\frac{5}{2}} + 3, - 30^{\frac{5}{2}} + 3$

Decimal Form:

$d = 4932.50301754 \dots, - 4926.50301754 \dots$