Pre-Algebra Examples

$\frac{{(t z^{- 3})}^{- 2}}{t^{- 3} z}$

Step 1

Move ${(t z^{- 3})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{t^{- 3} z {(t z^{- 3})}^{2}}$

Step 2

Move $t^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{t^{3}}{z {(t z^{- 3})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $t z^{- 3}$ .

$\frac{t^{3}}{z t^{2} {(z^{- 3})}^{2}}$

Step 3.2

Multiply the exponents in ${(z^{- 3})}^{2}$ .

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Step 3.2.1

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

$\frac{t^{3}}{z t^{2} z^{- 3 \cdot 2}}$

Step 3.2.2

Multiply $- 3$ by $2$ .

$\frac{t^{3}}{z t^{2} z^{- 6}}$

Step 3.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{t^{3}}{z t^{2} \frac{1}{z^{6}}}$

Step 3.4

Combine exponents.

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Step 3.4.1

Combine $z$ and $\frac{1}{z^{6}}$ .

$\frac{t^{3}}{t^{2} \frac{z}{z^{6}}}$

Step 3.4.2

Combine $t^{2}$ and $\frac{z}{z^{6}}$ .

$\frac{t^{3}}{\frac{t^{2} z}{z^{6}}}$

Step 3.5

Reduce the expression $\frac{t^{2} z}{z^{6}}$ by cancelling the common factors.

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Step 3.5.1

Factor $z$ out of $t^{2} z$ .

$\frac{t^{3}}{\frac{z t^{2}}{z^{6}}}$

Step 3.5.2

Factor $z$ out of $z^{6}$ .

$\frac{t^{3}}{\frac{z t^{2}}{z \cdot z^{5}}}$

Step 3.5.3

Cancel the common factor.

$\frac{t^{3}}{\frac{z t^{2}}{z \cdot z^{5}}}$

Step 3.5.4

Rewrite the expression.

$\frac{t^{3}}{\frac{t^{2}}{z^{5}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$t^{3} \frac{z^{5}}{t^{2}}$

Step 5

Cancel the common factor of $t^{2}$ .

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Step 5.1

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

$t^{2} t \frac{z^{5}}{t^{2}}$

Step 5.2

Cancel the common factor.

$t^{2} t \frac{z^{5}}{t^{2}}$

Step 5.3

Rewrite the expression.

$t z^{5}$