What is v^{(-2)}(2v^{(4)}+3v^{(2)}-2v^{(-3)}) ?

The solution to v^{(-2)}(2v^{(4)}+3v^{(2)}-2v^{(-3)}) is (2v^7+3v^5-2)/(v^5)

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simplify v^{(-2)}(2v^{(4)}+3v^{(2)}-2v^{(-3)})

simplify

v^{(- 2)} (2 v^{(4)} + 3 v^{(2)} - 2 v^{(- 3)})

\frac{2 v ^{7} + 3 v ^{5} - 2}{v ^{5}}

Solution steps

v^{- 2} (2 v^{4} + 3 v^{2} - 2 v^{- 3})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

v^{- 2} = \frac{1}{v ^{2}}

= \frac{1}{v ^{2}} (2 v^{4} + 3 v^{2} - 2 v^{- 3})

Simplify

2 v^{4} + 3 v^{2} - 2 v^{- 3} : 2 v^{4} + 3 v^{2} - \frac{2}{v ^{3}}

= \frac{1}{v ^{2}} (2 v^{4} + 3 v^{2} - \frac{2}{v ^{3}})

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot ( 2 v ^{4} + 3 v ^{2} - \frac{2}{v ^{3}} )}{v ^{2}}

Simplify

1 \cdot (2 v^{4} + 3 v^{2} - \frac{2}{v ^{3}}) : \frac{2 v ^{7} + 3 v ^{5} - 2}{v ^{3}}

= \frac{\frac{2 v ^{7} + 3 v ^{5} - 2}{v ^{3}}}{v ^{2}}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{2 v ^{7} + 3 v ^{5} - 2}{v ^{3} v ^{2}}

Simplify

v^{3} v^{2} : v^{5}

= \frac{2 v ^{7} + 3 v ^{5} - 2}{v ^{5}}

e^{2 x} (e^{- 2 x})

e^{(- 3 \cdot 3)} \cdot (- 4 \cdot (3) - 16)

6 x (4 x^{2})

e^{- \frac{x π}{1 - x ^{2}} = 0.25}

e^{- l n ∣ c o s (t) ∣}

What is v^{(-2)}(2v^{(4)}+3v^{(2)}-2v^{(-3)}) ?
The solution to v^{(-2)}(2v^{(4)}+3v^{(2)}-2v^{(-3)}) is (2v^7+3v^5-2)/(v^5)