Simplify (3t^-1)/(-3(t^-1)^4)

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

Step 1

Reduce the expression by cancelling the common factors.

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

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

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

Factor $3$ out of $3$ .

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

Cancel the common factors.

Factor $3$ out of $- 3 {(t^{- 1})}^{4} t$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{- {(t^{- 1})}^{4} t}$

Cancel the common factor of $1$ and $- 1$ .

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- {(t^{- 1})}^{4} t}$

Move the negative in front of the fraction.

$- \frac{1}{{(t^{- 1})}^{4} t}$

Step 2

Simplify the denominator.

Multiply the exponents in ${(t^{- 1})}^{4}$ .

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

$- \frac{1}{t^{- 1 \cdot 4} t}$

Multiply $- 1$ by $4$ .

$- \frac{1}{t^{- 4} t}$

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

$- \frac{1}{\frac{1}{t^{4}} t}$

Step 3

Simplify terms.

Combine $\frac{1}{t^{4}}$ and $t$ .

$- \frac{1}{\frac{t}{t^{4}}}$

Reduce the expression $\frac{t}{t^{4}}$ by cancelling the common factors.

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

$- \frac{1}{\frac{t^{1}}{t^{4}}}$

Factor $t$ out of $t^{1}$ .

$- \frac{1}{\frac{t \cdot 1}{t^{4}}}$

Factor $t$ out of $t^{4}$ .

$- \frac{1}{\frac{t \cdot 1}{t \cdot t^{3}}}$

Cancel the common factor.

$- \frac{1}{\frac{t \cdot 1}{t \cdot t^{3}}}$

Rewrite the expression.

$- \frac{1}{\frac{1}{t^{3}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$- (1 t^{3})$

Step 5

Multiply $t^{3}$ by $1$ .

$- t^{3}$

Simplify (3t^-1)/(-3(t^-1)^4)

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