Basic Math Examples

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

Step 1

Cancel the common factor of $k^{3 t + 2}$ and $k^{2 + 3 t}$ .

Tap for more steps...

Step 1.1

Factor $k^{2 + 3 t}$ out of $k^{3 t + 2}$ .

${(\frac{k^{2 + 3 t} k^{3 t + 2 - (2 + 3 t)}}{k^{2 + 3 t}})}^{10}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Multiply by $1$ .

${(\frac{k^{2 + 3 t} k^{3 t + 2 - (2 + 3 t)}}{k^{2 + 3 t} \cdot 1})}^{10}$

Step 1.2.2

Cancel the common factor.

${(\frac{k^{2 + 3 t} k^{3 t + 2 - (2 + 3 t)}}{k^{2 + 3 t} \cdot 1})}^{10}$

Step 1.2.3

Rewrite the expression.

${(\frac{k^{3 t + 2 - (2 + 3 t)}}{1})}^{10}$

Step 1.2.4

Divide $k^{3 t + 2 - (2 + 3 t)}$ by $1$ .

${(k^{3 t + 2 - (2 + 3 t)})}^{10}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Apply the distributive property.

${(k^{3 t + 2 - 1 \cdot 2 - (3 t)})}^{10}$

Step 2.2

Multiply $- 1$ by $2$ .

${(k^{3 t + 2 - 2 - (3 t)})}^{10}$

Step 2.3

Multiply $3$ by $- 1$ .

${(k^{3 t + 2 - 2 - 3 t})}^{10}$

Step 3

Simplify by adding terms.

Tap for more steps...

Step 3.1

Combine the opposite terms in $3 t + 2 - 2 - 3 t$ .

Tap for more steps...

Step 3.1.1

Subtract $2$ from $2$ .

${(k^{3 t + 0 - 3 t})}^{10}$

Step 3.1.2

Add $3 t$ and $0$ .

${(k^{3 t - 3 t})}^{10}$

Step 3.1.3

Subtract $3 t$ from $3 t$ .

${(k^{0})}^{10}$

Step 3.2

Simplify the expression.

Tap for more steps...

Step 3.2.1

Multiply the exponents in ${(k^{0})}^{10}$ .

Tap for more steps...

Step 3.2.1.1

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

$k^{0 \cdot 10}$

Step 3.2.1.2

Multiply $0$ by $10$ .

$k^{0}$

Step 3.2.2

Anything raised to $0$ is $1$ .

$1$