Question

1- Calcule:

a) 7²
b) 4³
c) 8¹
d) 9⁰
f) (— 9)²
g) (— 5)³
h) (— 1)⁷
i) (— 15)²
j) (— 10)⁰


2- Calcule:

a) 2⁵
b) (— 2)⁵
c) — 2⁵
d) 2⁴
e) (— 2)⁴
f) — 2⁴
g) — (— 3)⁴
h) — (— 5)³
i) — (+ 2)⁶


3- Calcule:

a) 7-²
b) 5-³
c) 2-⁴
d) 2-⁵
e) (— 3)-²
f) — (— 3)-²





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Answer 1

Explicação passo-a-passo:

1)

a)

$\sf 7^2=7\cdot7$

$\sf 7^2=\red{49}$

b)

$\sf 4^3=4\cdot4\cdot4$

$\sf 4^3=\red{64}$

c)

$\sf 8^1=\red{8}$

-> Todo número elevado a 1 é igual a ele mesmo

d)

$\sf 9^0=\red{1}$

-> Todo número elevado a zero é igual a 1 (exceto 0⁰, que é indeterminado)

f)

$\sf (-9)^2=(-9)\cdot(-9)$

$\sf (-9)^2=\red{81}$

g)

$\sf (-5)^3=(-5)\cdot(-5)\cdot(-5)$

$\sf (-5)^3=\red{-125}$

h)

$\sf (-1)^7=\red{-1}$

-> (-1) elevado a um expoente ímpar resulta em -1

-> (-1) elevado a um expoente par resulta em 1

i)

$\sf (-15)^2=(-15)\cdot(-15)$

$\sf (-15)^2=\red{225}$

j)

$\sf (-10)^0=\red{1}$

2)

a)

$\sf 2^5=2\cdot2\cdot2\cdot2\cdot2$

$\sf 2^5=\red{32}$

b)

$\sf (-2)^5=(-2)\cdot(-2)\cdot(-2)\cdot(-2)\cdot(-2)$

$\sf (-2)^5=\red{-32}$

c)

$\sf -2^5=-2\cdot2\cdot2\cdot2\cdot2$

$\sf -2^5=\red{-32}$

d)

$\sf 2^4=2\cdot2\cdot2\cdot2$

$\sf 2^4=\red{16}$

e)

$\sf (-2)^4=(-2)\cdot(-2)\cdot(-2)\cdot(-2)$

$\sf (-2)^4=\red{16}$

f)

$\sf -2^4=-2\cdot2\cdot2\cdot2$

$\sf -2^4=\red{-16}$

g)

$\sf -(-3)^4=-(-3)\cdot(-3)\cdot(-3)\cdot(-3)$

$\sf -(-3)^4=\red{-81}$

h)

$\sf -(-5)^3=-(-5)\cdot(-5)\cdot(-5)$

$\sf -(-5)^3=-(-125)$

$\sf -(-5)^3=\red{125}$

i)

$\sf -(+2)^6=-(+2)\cdot(+2)\cdot(+2)\cdot(+2)\cdot(+2)\cdot(+2)$

$\sf -(+2)^6=\red{-64}$

3)

a)

$\sf 7^{-2}=\dfrac{1}{7}\cdot\dfrac{1}{7}$

$\sf 7^{-2}=\red{\dfrac{1}{49}}$

b)

$\sf 5^{-3}=\dfrac{1}{5}\cdot\dfrac{1}{5}\cdot\dfrac{1}{5}$

$\sf 5^{-3}=\red{\dfrac{1}{125}}$

c)

$\sf 2^{-4}=\dfrac{1}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}$

$\sf 2^{-4}=\red{\dfrac{1}{16}}$

d)

$\sf 2^{-5}=\dfrac{1}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}\cdot\dfrac{1}{2}$

$\sf 2^{-5}=\red{\dfrac{1}{32}}$

e)

$\sf (-3)^{-2}=\left(-\dfrac{1}{3}\right)\cdot\left(-\dfrac{1}{3}\right)$

$\sf (-3)^{-2}=\red{\dfrac{1}{9}}$

f)

$\sf -(-3)^{-2}=-\left(-\dfrac{1}{3}\right)\cdot\left(-\dfrac{1}{3}\right)$

$\sf -(-3)^{-2}=\red{-\dfrac{1}{9}}$

Answer 2

Oie, Td Bom?!

1.

a)

$7 {}^{2} = 7 \: . \: 7 = 49$

b)

$4 {}^{3} = 4 \: . \: 4 \: . \: 4 = 64$

c)

$8 {}^{1} = 8$

d)

$9 {}^{0} = 1$

f)

$( - 9) {}^{2} = 9 {}^{2} = 9 \: . \: 9 = 81$

g)

$( - 5) {}^{3} = - 5 {}^{3} = - (5 \: . \: 5 \: . \: 5) = - 125$

h)

$( - 1) {}^{7} = - 1 {}^{7} = - 1$

i)

$( - 15) {}^{2} = 15 {}^{2} = 15 \: . \: 15 = 225$

j)

$( - 10) {}^{0} = 1$

2.

a)

$2 {}^{5} = 2 \: . \: 2 \: . \: 2 \: . \: 2 \: . \: 2 = 32$

b)

$( - 2) {}^{5} = - 2 {}^{5} = - (2 \: . \: 2 \: . \: 2 \: . \: 2 \: . \: 2) = - 32$

c)

$- 2 {}^{5} = - 2 \: . \: 2 \: . \: 2 \: . \: 2 \: . \: 2 = - 32$

d)

$2 {}^{4} = 2 \: . \: 2 \: . \: 2 \: . \: 2 = 16$

e)

$( - 2) {}^{4} = 2 {}^{4} = 2 \: . \: 2 \: . \: 2 \: . \: 2 = 16$

f)

$- 2 {}^{4} = - 2 \: . \: 2 \: . \: 2 \: . \: 2 = - 16$

g)

$- ( - 3) {}^{4} = - 3 {}^{4} = - 3 \: . \: 3 \: . \: 3 \: . \: 3 = - 81$

h)

$- ( - 5) {}^{3} = - ( - 5 {}^{3} ) = - ( - (5 \: . \: 5 \: . \: 5)) = - ( - 125) = 125$

i)

$- 2 {}^{6} = - 2 \: . \: 2 \: . \: 2 \: . \: 2 \: . \: 2 \: . \: 2 = - 64$

3.

a)

$7 {}^{ - 2} = \frac{1}{7 {}^{2} } = \frac{1}{49}$

b)

$5 {}^{ - 3} = \frac{1}{5 {}^{3} } = \frac{1}{125}$

c)

$2 {}^{ - 4} = \frac{1}{2 {}^{4} } = \frac{1}{16}$

d)

$2 {}^{ - 5} = \frac{1}{2 {}^{5} } = \frac{1}{32}$

e)

$( - 3) {}^{ - 2} = 3 {}^{ - 2} = \frac{1}{3 {}^{2} } = \frac{1}{9}$

f)

$- ( - 3) {}^{ - 2} = - 3 {}^{ - 2} = - \frac{1}{3 {}^{2} } = - \frac{1}{9}$

Att. Makaveli1996