Question

aplique as propriedades da potenciação e reduza em uma unica potência

a)
$10 {}^{5} \times 10 {}^{4}$
b)
$(10 {}^{4} ) {}^{6}$
d)
$(10000) {}^{5}$
e)
$100 \times 0.01 \times 1000 \div 0.0001 =$
f)
$( \frac{1}{10000} {}^{ - 6} =$
​

Answer 1

a -

$10^5\cdot10^4\\10^{5+4}\\10^{9}$

b -

$(10^4)^6\\10^{4\cdot6}\\10^{24}$

c -

$(10000)^5\\(10^4)^5\\10^{4\cdot5}\\10^{20}$

d -

$100\cdot0,01\cdot\dfrac{1000}{0,0001}\\10^2\cdot10^{-2}\cdot\dfrac{10^{3}}{10^{-4}}\\10^{2+(-2)}\cdot10^{3-(-4)}\\10^0\cdot10^{7}\\1\cdot10^{7}\\10^{7}$

e -

$\left(\dfrac{1}{10000}\right)^{-6}\\\left(\dfrac{1}{10^4}\right)^{-6}\\(10^{-4})^{-6}\\10^{(-4).(-6)}\\10^{24}$

Propriedades utilizadas:

• $x^a\cdot x^b=x^{a+b}$

• $\dfrac{x^a}{x^b}=x^{a-b}$

• $(x^a)^b=x^{a\cdotb}$

Dúvidas só perguntar!