Algebra Examples

$\frac{1}{2} {(4 k^{5})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $4 k^{5}$ .

$\frac{1}{2} \cdot (4^{2} {(k^{5})}^{2})$

Step 1.2

Raise $4$ to the power of $2$ .

$\frac{1}{2} \cdot (16 {(k^{5})}^{2})$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $16 {(k^{5})}^{2}$ .

$\frac{1}{2} \cdot (2 (8 {(k^{5})}^{2}))$

Step 2.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 (8 {(k^{5})}^{2}))$

Step 2.3

Rewrite the expression.

$8 {(k^{5})}^{2}$

Step 3

Multiply the exponents in ${(k^{5})}^{2}$ .

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Step 3.1

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

$8 k^{5 \cdot 2}$

Step 3.2

Multiply $5$ by $2$ .

$8 k^{10}$