Algebra Examples

$\frac{- 3 {(h^{3} t^{- 5})}^{- 3}}{6 h^{4}}$

Step 1

Move ${(h^{3} t^{- 5})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 3}{6 h^{4} {(h^{3} t^{- 5})}^{3}}$

Step 2

Cancel the common factor of $- 3$ and $6$ .

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Step 2.1

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{6 h^{4} {(h^{3} t^{- 5})}^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $6 h^{4} {(h^{3} t^{- 5})}^{3}$ .

$\frac{3 (- 1)}{3 (2 h^{4} {(h^{3} t^{- 5})}^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{3 \cdot - 1}{3 (2 h^{4} {(h^{3} t^{- 5})}^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{- 1}{2 h^{4} {(h^{3} t^{- 5})}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $h^{3} t^{- 5}$ .

$\frac{- 1}{2 h^{4} {(h^{3})}^{3} {(t^{- 5})}^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{- 1}{2 h^{4} h^{3 \cdot 3} {(t^{- 5})}^{3}}$

Step 3.2.2

Multiply $3$ by $3$ .

$\frac{- 1}{2 h^{4} h^{9} {(t^{- 5})}^{3}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{- 1}{2 h^{4} h^{9} t^{- 5 \cdot 3}}$

Step 3.3.2

Multiply $- 5$ by $3$ .

$\frac{- 1}{2 h^{4} h^{9} t^{- 15}}$

Step 3.4

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

$\frac{- 1}{2 h^{4} h^{9} \frac{1}{t^{15}}}$

Step 3.5

Combine exponents.

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Step 3.5.1

Multiply $h^{4}$ by $h^{9}$ by adding the exponents.

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Step 3.5.1.1

Move $h^{9}$ .

$\frac{- 1}{2 (h^{9} h^{4}) \frac{1}{t^{15}}}$

Step 3.5.1.2

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

$\frac{- 1}{2 h^{9 + 4} \frac{1}{t^{15}}}$

Step 3.5.1.3

Add $9$ and $4$ .

$\frac{- 1}{2 h^{13} \frac{1}{t^{15}}}$

Step 3.5.2

Combine $2$ and $\frac{1}{t^{15}}$ .

$\frac{- 1}{h^{13} \frac{2}{t^{15}}}$

Step 3.5.3

Combine $h^{13}$ and $\frac{2}{t^{15}}$ .

$\frac{- 1}{\frac{h^{13} \cdot 2}{t^{15}}}$

Step 3.6

Move $2$ to the left of $h^{13}$ .

$\frac{- 1}{\frac{2 h^{13}}{t^{15}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- \frac{t^{15}}{2 h^{13}}$