Question

Calcule as potências de expoente negativo
a) 7⁻¹
b) (1/5)⁻²
c) (-0,5)⁻⁴
d) (5/9)⁻¹
e) (-3/8)⁻¹
f) (-3)⁻¹
g) (-3/2)⁻²
h) (7/4)⁻²
i) 10⁻²
j) (-1)⁻5
k) (1/100)⁻¹
l) - (-0,1)⁻⁴

Answer 1

a) $7^{-1}=\dfrac{1}{7^1}=\dfrac{1}{7}$

b) $\left(\dfrac{1}{5}\right)^{-2}=5^2=25$

c) $(-0,5)^{-4}=\left(-\dfrac{1}{2}\right)^{-4}=(-2)^{4}=16$

d) $\left(\dfrac{5}{9}\right)^{-1}=\left(\dfrac{9}{5}\right)^{1}=\dfrac{9}{5}$

e) $\left(-\dfrac{3}{8}\right)^{-1}=\left(\dfrac{8}{3}\right)^{1}=\dfrac{8}{3}$

f) $(-3)^{-1}=\left(-\dfrac{1}{3}\right)^{1}=-\dfrac{1}{3}$

g) $\left(-\dfrac{3}{2}\right)^{-2}=\left(-\dfrac{2}{3}\right)^{2}=\dfrac{4}{9}$

h) $\left(\dfrac{7}{4}\right)^{-2}=\left(\dfrac{4}{7}\right)^2=\dfrac{16}{49}$

i) $10^{-2}=\left(\dfrac{1}{10}\right)^2=\dfrac{1}{100}$

j) $(-1)^{-5}=\left(-\dfrac{1}{1}\right)^{5}=-1$

k) $\left(\dfrac{1}{100}\right)^{-1}=100^{1}=100$

l) $-(-0,1)^{-4}=-\left(-\dfrac{1}{10}\right)^{-4}=-(-10)^{-4}=-10.000$.