What is [((-1001/115)^5)^{16}]^{100} ?

The solution to [((-1001/115)^5)^{16}]^{100} is (1001^{8000})/(115^{8000)}

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simplify [((-1001/115)^5)^{16}]^{100}

simplify

((- \frac{1001}{115})^{5})^{16}^{100}

\frac{100 1 ^{8000}}{11 5 ^{8000}}

Solution steps

((- \frac{1001}{115})^{5})^{16}^{100}

((- \frac{1001}{115})^{5})^{16} : (- \frac{1001}{115})^{80}

= [(- \frac{1001}{115})^{80}]^{100}

(- \frac{1001}{115})^{80} = \frac{100 1 ^{80}}{11 5 ^{80}}

= (\frac{100 1 ^{80}}{11 5 ^{80}})^{100}

Apply exponent rule:

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

= \frac{( 100 1 ^{80} ) ^{100}}{( 11 5 ^{80} ) ^{100}}

(11 5^{80})^{100} : 11 5^{8000}

= \frac{( 100 1 ^{80} ) ^{100}}{11 5 ^{8000}}

(100 1^{80})^{100} : 100 1^{8000}

= \frac{100 1 ^{8000}}{11 5 ^{8000}}

e^{- 8 t}

[(2^{3})^{- 2}]^{0.5} \cdot [(0.5)^{0.75}]^{- 4}

e^{- 3 (t - 2)}

- \frac{1}{2} e^{- 3}

What is [((-1001/115)^5)^{16}]^{100} ?
The solution to [((-1001/115)^5)^{16}]^{100} is (1001^{8000})/(115^{8000)}