Question

HELP!! preciso entregar essa tarefa amanhã é urgente​

Answer 1

a)

$2^5 \cdot (2 \cdot 5)^5 \cdot (2 \cdot 2 \cdot 5)^{-3}$

$2^5 \cdot 2^5 \cdot 5^5 \cdot 2^{-3} \cdot 2^{-3} \cdot 5^{-3}$

$2^{5+5-3-3} \cdot 5^{5-3}$

$2^{4} \cdot 5^{2}$

$16 \cdot 25$

$\boxed{400}$

b)

$\left(\dfrac{8^2}{2^2} \cdot 4^3 \right)^{10}$

$\left(\dfrac{(2^3)^2}{2^2} \cdot (2^2)^3 \right)^{10}$

$\left(\dfrac{2^6}{2^2} \cdot 2^6 \right)^{10}$

$\left(2^4 \cdot 2^6 \right)^{10}$

$\left(2^{10}\right)^{10}$

$\boxed{2^{100}}$

c)

$\dfrac{5^{-2-2}}{5^{8-5}}$

$\dfrac{5^{-4}}{5^{3}}$

$\dfrac{1}{5^{4} \cdot 5^{3}}$

$\dfrac{1}{5^{4+3}}$

$\dfrac{1}{5^{7}}$

$\boxed{5^{-7}}$