Algebra Examples

$\frac{4 z^{- 1}}{- 3 {(z^{5})}^{3}}$

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

Multiply the exponents in ${(z^{5})}^{3}$ .

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Step 2.1.1

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

$\frac{4}{- 3 z^{5 \cdot 3} z}$

Step 2.1.2

Multiply $5$ by $3$ .

$\frac{4}{- 3 z^{15} z}$

Step 2.2

Combine exponents.

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Step 2.2.1

Raise $z$ to the power of $1$ .

$\frac{4}{- 3 (z^{1} z^{15})}$

Step 2.2.2

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

$\frac{4}{- 3 z^{1 + 15}}$

Step 2.2.3

Add $1$ and $15$ .

$\frac{4}{- 3 z^{16}}$

Step 3

Move the negative in front of the fraction.

$- \frac{4}{3 z^{16}}$