Write the Fraction in Simplest Form ((2v^-4t^-1)^-5)/(4v^-1t)

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

Move ${(2 v^{- 4} t^{- 1})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

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

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

Simplify the denominator.

Apply the product rule to $2 v^{- 4} t^{- 1}$ .

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

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

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

Combine $2$ and $\frac{1}{v^{4}}$ .

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

Apply the product rule to $\frac{2}{v^{4}}$ .

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

Raise $2$ to the power of $5$ .

$\frac{v}{4 t \frac{32}{{(v^{4})}^{5}} {(t^{- 1})}^{5}}$

Multiply the exponents in ${(v^{4})}^{5}$ .

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

$\frac{v}{4 t \frac{32}{v^{4 \cdot 5}} {(t^{- 1})}^{5}}$

Multiply $4$ by $5$ .

$\frac{v}{4 t \frac{32}{v^{20}} {(t^{- 1})}^{5}}$

Multiply the exponents in ${(t^{- 1})}^{5}$ .

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

$\frac{v}{4 t \frac{32}{v^{20}} t^{- 1 \cdot 5}}$

Multiply $- 1$ by $5$ .

$\frac{v}{4 t \frac{32}{v^{20}} t^{- 5}}$

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

$\frac{v}{4 t \frac{32}{v^{20}} \frac{1}{t^{5}}}$

Combine exponents.

Combine $4$ and $\frac{32}{v^{20}}$ .

$\frac{v}{t \frac{4 \cdot 32}{v^{20}} \frac{1}{t^{5}}}$

Multiply $4$ by $32$ .

$\frac{v}{t \frac{128}{v^{20}} \frac{1}{t^{5}}}$

Combine $t$ and $\frac{128}{v^{20}}$ .

$\frac{v}{\frac{t \cdot 128}{v^{20}} \cdot \frac{1}{t^{5}}}$

Multiply $\frac{t \cdot 128}{v^{20}}$ by $\frac{1}{t^{5}}$ .

$\frac{v}{\frac{t \cdot 128}{v^{20} t^{5}}}$

Reduce the expression $\frac{t \cdot 128}{v^{20} t^{5}}$ by cancelling the common factors.

Factor $t$ out of $t \cdot 128$ .

$\frac{v}{\frac{t (128)}{v^{20} t^{5}}}$

Factor $t$ out of $v^{20} t^{5}$ .

$\frac{v}{\frac{t (128)}{t (v^{20} t^{4})}}$

Cancel the common factor.

$\frac{v}{\frac{t \cdot 128}{t (v^{20} t^{4})}}$

Rewrite the expression.

$\frac{v}{\frac{128}{v^{20} t^{4}}}$

Multiply the numerator by the reciprocal of the denominator.

$v \frac{v^{20} t^{4}}{128}$

Multiply $v \frac{v^{20} t^{4}}{128}$ .

Combine $v$ and $\frac{v^{20} t^{4}}{128}$ .

$\frac{v (v^{20} t^{4})}{128}$

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

$\frac{v^{20} v^{1} t^{4}}{128}$

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

$\frac{v^{20 + 1} t^{4}}{128}$

Add $20$ and $1$ .

$\frac{v^{21} t^{4}}{128}$

Write the Fraction in Simplest Form ((2v^-4t^-1)^-5)/(4v^-1t)

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