Algebra Examples

$(4 k) {(\frac{3 k^{- 5}}{3 k^{5}})}^{2}$

Step 1

Move $k^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 k {(\frac{3}{3 k^{5} k^{5}})}^{2}$

Step 2

Multiply $k^{5}$ by $k^{5}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $k^{5}$ .

$4 k {(\frac{3}{3 (k^{5} k^{5})})}^{2}$

Step 2.2

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

$4 k {(\frac{3}{3 k^{5 + 5}})}^{2}$

Step 2.3

Add $5$ and $5$ .

$4 k {(\frac{3}{3 k^{10}})}^{2}$

Step 3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$4 k {(\frac{3}{3 k^{10}})}^{2}$

Step 3.2

Rewrite the expression.

$4 k {(\frac{1}{k^{10}})}^{2}$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Apply the product rule to $\frac{1}{k^{10}}$ .

$4 k \frac{1^{2}}{{(k^{10})}^{2}}$

Step 4.2

One to any power is one.

$4 k \frac{1}{{(k^{10})}^{2}}$

Step 4.3

Multiply the exponents in ${(k^{10})}^{2}$ .

Tap for more steps...

Step 4.3.1

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

$4 k \frac{1}{k^{10 \cdot 2}}$

Step 4.3.2

Multiply $10$ by $2$ .

$4 k \frac{1}{k^{20}}$

Step 5

Cancel the common factor of $k$ .

Tap for more steps...

Step 5.1

Factor $k$ out of $4 k$ .

$k \cdot 4 \frac{1}{k^{20}}$

Step 5.2

Factor $k$ out of $k^{20}$ .

$k \cdot 4 \frac{1}{k \cdot k^{19}}$

Step 5.3

Cancel the common factor.

$k \cdot 4 \frac{1}{k \cdot k^{19}}$

Step 5.4

Rewrite the expression.

$4 \frac{1}{k^{19}}$

Step 6

Combine $4$ and $\frac{1}{k^{19}}$ .

$\frac{4}{k^{19}}$