Precalculus Examples

$87.6 = 0.2 x^{\frac{3}{2}}$

Step 1

Rewrite the equation as $0.2 x^{\frac{3}{2}} = 87.6$ .

$0.2 x^{\frac{3}{2}} = 87.6$

Step 2

Divide each term in $0.2 x^{\frac{3}{2}} = 87.6$ by $0.2$ and simplify.

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Step 2.1

Divide each term in $0.2 x^{\frac{3}{2}} = 87.6$ by $0.2$ .

$\frac{0.2 x^{\frac{3}{2}}}{0.2} = \frac{87.6}{0.2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor.

$\frac{0.2 x^{\frac{3}{2}}}{0.2} = \frac{87.6}{0.2}$

Step 2.2.2

Divide $x^{\frac{3}{2}}$ by $1$ .

$x^{\frac{3}{2}} = \frac{87.6}{0.2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $87.6$ by $0.2$ .

$x^{\frac{3}{2}} = 438$

Step 3

Raise each side of the equation to the power of $\frac{2}{3}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{3}{2}})}^{\frac{2}{3}} = 438^{\frac{2}{3}}$

Step 4

Simplify the left side.

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Step 4.1

Simplify ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 4.1.1

Multiply the exponents in ${(x^{\frac{3}{2}})}^{\frac{2}{3}}$ .

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Step 4.1.1.1

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

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 438^{\frac{2}{3}}$

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Cancel the common factor.

$x^{\frac{3}{2} \cdot \frac{2}{3}} = 438^{\frac{2}{3}}$

Step 4.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{2} \cdot 2} = 438^{\frac{2}{3}}$

Step 4.1.1.3

Cancel the common factor of $2$ .

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Step 4.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 438^{\frac{2}{3}}$

Step 4.1.1.3.2

Rewrite the expression.

$x^{1} = 438^{\frac{2}{3}}$

Step 4.1.2

Simplify.

$x = 438^{\frac{2}{3}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 438^{\frac{2}{3}}$

Decimal Form:

$x = 57.67435420 \dots$