Question

Reduza a uma única potência.

a) [(-22)

2] =

b) 4 =

8

c) 52 . 55 . 5-1 =

d)2² . 4³. 8¹ =

e) 10² . 10³. 104 . 109=​

Answer 1

Explicação passo-a-passo:

1.

a) $[(-2)^2]^2=(-2)^{2\cdot2}=(-2)^4$

b) $\dfrac{4}{8}=\dfrac{2^2}{2^3}=2^{2-3}=2^{-1}$

c) $5^2\cdot5^5\cdot5^{-1}=5^{2+5-1}=5^{6}$

d) Veja que $4=2^2$ e $8=2^3$. Assim:

$4^3=(2^2)^3=2^{2\cdot3}=2^6$

Temos que:

$2^2\cdot4^3\cdot8^1=2^2\cdot2^6\cdot2^3=2^{2+6+3}=2^{11}$

e) $10^2\cdot10^3\cdot10^4\cdot10^9=10^{2+3+4+9}=10^{18}$

2.

$\dfrac{2^2\cdot2^7\cdot2^1}{2^4\cdot2^3}=\dfrac{2^{2+7+1}}{2^{4+3}}=\dfrac{2^{10}}{2^7}=2^{10-7}=2^3$

Letra A

Answer 2

Explicação passo-a-passo:

Olá!!!

Potênciacão

a) [(-2²)²]=

$\boxed{{ ( - 4)}^{2} \rightarrow \: ( - 4) \times ( -4 ) = \boxed{16}}$

b)4/8

$\boxed{{ \frac{ {2}^{2} }{ {2}^{3} }} \rightarrow \: {2}^{(2 - 3)} = \boxed{ {2}^{ - 1} }}$

c)5² x 5^5 x 5-¹

$\boxed{ {5}^{(2 + 5 + ( - 1))} \rightarrow \: {5}^{7 - 1} = \boxed{ {5}^{6} }}$

d)2²x4³x8¹

$\boxed{ {2}^{2} \times { ({2}^{2}) }^{3} \times { ({2}^{3} )}^{1} \rightarrow \: {2}^{2} \times {2}^{6} \times {2}^{3} = > {2}^{(2 + 6 + 3)} = \boxed{ {2}^{11} }}$

e) 10²x10³x10⁴x10⁹

$\boxed{ {10}^{(2 + 3 + 4 + 9)} \rightarrow \: {10}^{9 + 9} = \boxed{ {10}^{18} }}$

2)

$\frac{ {2}^{2} \times {2}^{7} \times {2}^{1} }{ {2}^{4} \times {2}^{3} } \\ \\ \frac{ {2}^{(2 + 7 + 1)} }{ {2}^{(4 + 3)} } \\ \\ \frac{ {2}^{10} }{ {2}^{7} } \\ \\ {2}^{(10 - 7)} \\ \\ \checkmark\boxed{\boxed{ \Rightarrow {2}^{3} }}$