Question

Simplifiquem :
(5²)² e (3³) -² e (0,2-²) -⁴

4 elevado 6 ÷ 4² e 3² ÷ 3-³

7-² ÷ (7-³)²

Answer 1

$a) (5^2)^2 = 5^{2\times2}=5^4\\\\b) (3^2)^{-3}=3^{-2\times3}=3^{-6}}=\frac{1}{3^6}\\\\c)\frac{4^6}{4^2}=4^{6-2}=4^4\\\\d)(0.2^{-2})^{-4}=(\frac{1}{0.2^2})^{-4}= \left(\frac{1}{(\frac{1}{5})^2}\right)^{-4} = \left(\frac{1}{\frac{1}{5^2}}\right)^{-4}\\=\left(\frac{1}{\frac{1}{25}}\right)^{-4}= (25)^{-4}=\frac{1}{25^4}=\frac{1}{390625}\\\\=0.00000256=2.56\times10^{-6}\\\\e)\frac{3^2}{3^{-3}}=3^{2-(-3)}=3^5\\\\f)\frac{7^{-2}}{(7^{-3})^2}=\frac{7^{-2}}{7^{-3\times2}}=\frac{7^{-2}}{7^{-6}}=7^{-2-(-6)}=7^4$