Algebra Examples

${(12^{\frac{3}{5}} \cdot 8^{\frac{3}{5}})}^{5}$

Step 1

Apply the product rule to $12^{\frac{3}{5}} \cdot 8^{\frac{3}{5}}$ .

${(12^{\frac{3}{5}})}^{5} \cdot {(8^{\frac{3}{5}})}^{5}$

Step 2

Multiply the exponents in ${(12^{\frac{3}{5}})}^{5}$ .

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Step 2.1

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

$12^{\frac{3}{5} \cdot 5} \cdot {(8^{\frac{3}{5}})}^{5}$

Step 2.2

Cancel the common factor of $5$ .

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Step 2.2.1

Cancel the common factor.

$12^{\frac{3}{5} \cdot 5} \cdot {(8^{\frac{3}{5}})}^{5}$

Step 2.2.2

Rewrite the expression.

$12^{3} \cdot {(8^{\frac{3}{5}})}^{5}$

Step 3

Raise $12$ to the power of $3$ .

$1728 \cdot {(8^{\frac{3}{5}})}^{5}$

Step 4

Multiply the exponents in ${(8^{\frac{3}{5}})}^{5}$ .

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Step 4.1

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

$1728 \cdot 8^{\frac{3}{5} \cdot 5}$

Step 4.2

Cancel the common factor of $5$ .

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Step 4.2.1

Cancel the common factor.

$1728 \cdot 8^{\frac{3}{5} \cdot 5}$

Step 4.2.2

Rewrite the expression.

$1728 \cdot 8^{3}$

Step 5

Raise $8$ to the power of $3$ .

$1728 \cdot 512$

Step 6

Multiply $1728$ by $512$ .

$884736$