Algebra Examples

${(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})}^{2}$

Step 1

Apply the product rule to $6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}}$ .

${(6^{\frac{1}{2}})}^{2} \cdot {(4^{\frac{1}{3}})}^{2}$

Step 2

Multiply the exponents in ${(6^{\frac{1}{2}})}^{2}$ .

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Step 2.1

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

$6^{\frac{1}{2} \cdot 2} \cdot {(4^{\frac{1}{3}})}^{2}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Cancel the common factor.

$6^{\frac{1}{2} \cdot 2} \cdot {(4^{\frac{1}{3}})}^{2}$

Step 2.2.2

Rewrite the expression.

$6^{1} \cdot {(4^{\frac{1}{3}})}^{2}$

Step 3

Evaluate the exponent.

$6 \cdot {(4^{\frac{1}{3}})}^{2}$

Step 4

Multiply the exponents in ${(4^{\frac{1}{3}})}^{2}$ .

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Step 4.1

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

$6 \cdot 4^{\frac{1}{3} \cdot 2}$

Step 4.2

Combine $\frac{1}{3}$ and $2$ .

$6 \cdot 4^{\frac{2}{3}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$6 \cdot 4^{\frac{2}{3}}$

Decimal Form:

$15.11905259 \dots$