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Popular >

simplify (l^t-l^{-t})^3

Solution

simplify

(l^{t} - l^{- t})^{3}

Solution

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

Solution steps

(l^{t} - l^{- t})^{3}

Simplify

l^{t} - l^{- t} : \frac{l ^{2 t} - 1}{l ^{t}}

= (\frac{l ^{2 t} - 1}{l ^{t}})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( l ^{2 t} - 1 ) ^{3}}{( l ^{t} ) ^{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(l^{t})^{3} = l^{t \cdot 3}

= \frac{( l ^{2 t} - 1 ) ^{3}}{l ^{t \cdot 3}}

= \frac{( l ^{2 t} - 1 ) ^{3}}{l ^{3 t}}

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Frequently Asked Questions (FAQ)

What is (l^t-l^{-t})^3 ?
The solution to (l^t-l^{-t})^3 is ((l^{2t}-1)^3)/(l^{3t)}