Algebra Examples

$\frac{x}{\sqrt[3]{0.5 t}} = \sqrt[3]{0.2 t}$

Step 1

Multiply both sides by $\sqrt[3]{0.5 t}$ .

$\frac{x}{\sqrt[3]{0.5 t}} \sqrt[3]{0.5 t} = \sqrt[3]{0.2 t} \sqrt[3]{0.5 t}$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $\sqrt[3]{0.5 t}$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x}{\sqrt[3]{0.5 t}} \sqrt[3]{0.5 t} = \sqrt[3]{0.2 t} \sqrt[3]{0.5 t}$

Step 2.1.1.2

Rewrite the expression.

$x = \sqrt[3]{0.2 t} \sqrt[3]{0.5 t}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $\sqrt[3]{0.2 t} \sqrt[3]{0.5 t}$ .

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Step 2.2.1.1

Combine using the product rule for radicals.

$x = \sqrt[3]{0.2 t (0.5 t)}$

Step 2.2.1.2

Multiply $0.5$ by $0.2$ .

$x = \sqrt[3]{0.1 t \cdot t}$

Step 2.2.1.3

Raise $t$ to the power of $1$ .

$x = \sqrt[3]{0.1 (t^{1} t)}$

Step 2.2.1.4

Raise $t$ to the power of $1$ .

$x = \sqrt[3]{0.1 (t^{1} t^{1})}$

Step 2.2.1.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \sqrt[3]{0.1 t^{1 + 1}}$

Step 2.2.1.6

Add $1$ and $1$ .

$x = \sqrt[3]{0.1 t^{2}}$