Question

To what power do you have to raise:

a) 3 to get 27?
to
b) 2 to get 32?
CO
c) 5 to get 625?
d) 64 to get 8?
e) 81 to get 3?
f) 64 to get 2?
g) x² to get x??
h) x to get x12?
10
i) x to get xa?

Answer 1

Explanation:

a) 27 = 3 × 3 × 3 = 3³ Answer: 3

b) 32 = 2 × 2 × 2 × 2 × 2 =
`2^5` Answer: 5

c) 625 = 5 × 5 × 5 × 5 =
`5^4` Answer: 4

d)
`√(64) = 8` ⇒
`64^{(1)/(2)}` Answer: 1/2

e)
`\sqrt[4]{81}=3` ⇒
`81^{(1)/(4)}` Answer: 1/4

f)
`\sqrt[6]{64} =2` ⇒
`64^{(1)/(6) }` Answer: 1/6

g)
`(x^2)^{(1)/(2)}=x^1=x` Answer: 1/2

h)
`(x^3)^(4)=x^(12)` Answer: 4

i)
`(x)^8=x^8` Answer: 8

Answer 2

Explanation:

Prime factorize 27,32,625,

a) 27 = 3 * 3 * 3 = 3³

b) 32 = 2 * 2 * 2 * 2 *2 = 2⁵

c) 625 = 5*5*5*5 = 5⁴

`d) √(64)= (8^(2))^{(1)/(2)} = 8\\\\ e) \sqrt[4]{81}=\sqrt[4]{3*3*3*3}=(3^(4))^{(1)/(4)} = 3\\\\ f) \sqrt[6]{64}=\sqrt[6]{2*2*2*2*2*2}=(2^(6))^{(1)/(6)}=2\\\\ g)\sqrt{x^(2)}=(x^(2))^{(1)/(2)}=x\\\\`

`h) x^(12) = x^(3*4)= (x^(3))^(4)\\\\ i)x^(8)=x^(1*8)=(x^(1))^(8)`