Question

4 ) calcule as propriedades das potências

a) 8³ . 8².8⁵
b) 6¹⁰ : 6²:6⁴
c) (2⁵)²
d) 4⁸.4²:4⁵
e)5-¹​

Answer 1

a) 8³ . 8².8⁵

$8^3\cdot \:8^2\cdot \:8^5\\\\8^3\cdot \:8^2\cdot \:8^5=8^{3+2+5}\\\\=8^{3+2+5}\\\\\:3+2+5=10\\=8^{10}$

$=1073741824$

b) 6¹⁰ : 6²:6⁴

$\frac{\frac{6^{10}}{6^2}}{6^4}\\\\=\frac{6^{10}}{6^2\cdot \:6^4}\\\\=\frac{6^8}{6^4}\\\\=\frac{2^8\cdot \:3^8}{2^4\cdot \:3^4}\\\\=2^4\cdot \:3^4\\\\=3^4\cdot \:16\\\\=16\cdot \:81\\\\=1296$

c) (2⁵)²

$\left(2^5\right)^2\\\\\left(2^5\right)^2=2^{5\cdot \:2}\\\\=2^{5\cdot \:2}\\\\=2^{10}\\\\2^{10}=1024\\=1024$

d) 4⁸.4²:4⁵

$\frac{4^8\cdot \:4^2}{4^5}\\\\\frac{4^8}{4^5}=4^{8-5}\\=4^{8-5}\cdot \:4^2\\\\8-5=3\\=4^3\cdot \:4^2\\\\=1024$

e)5-¹​

$5-^1\\= 5$