Finite Math Examples

$- 5 k {(\frac{5}{2 k^{4} k^{5}})}^{0}$

Step 1

Multiply $k^{4}$ by $k^{5}$ by adding the exponents.

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Step 1.1

Move $k^{5}$ .

$- 5 k {(\frac{5}{2 (k^{5} k^{4})})}^{0}$

Step 1.2

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

$- 5 k {(\frac{5}{2 k^{5 + 4}})}^{0}$

Step 1.3

Add $5$ and $4$ .

$- 5 k {(\frac{5}{2 k^{9}})}^{0}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $\frac{5}{2 k^{9}}$ .

$- 5 k \frac{5^{0}}{{(2 k^{9})}^{0}}$

Step 2.2

Apply the product rule to $2 k^{9}$ .

$- 5 k \frac{5^{0}}{2^{0} {(k^{9})}^{0}}$

Step 3

Anything raised to $0$ is $1$ .

$- 5 k \frac{1}{2^{0} {(k^{9})}^{0}}$

Step 4

Simplify the denominator.

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Step 4.1

Anything raised to $0$ is $1$ .

$- 5 k \frac{1}{1 {(k^{9})}^{0}}$

Step 4.2

Multiply the exponents in ${(k^{9})}^{0}$ .

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Step 4.2.1

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

$- 5 k \frac{1}{1 k^{9 \cdot 0}}$

Step 4.2.2

Multiply $9$ by $0$ .

$- 5 k \frac{1}{1 k^{0}}$

Step 4.3

Anything raised to $0$ is $1$ .

$- 5 k \frac{1}{1 \cdot 1}$

Step 4.4

Multiply $1$ by $1$ .

$- 5 k \frac{1}{1}$

Step 5

Simplify the expression.

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Step 5.1

Divide $1$ by $1$ .

$- 5 k \cdot 1$

Step 5.2

Multiply $- 5$ by $1$ .

$- 5 k$