Question

Rewrite the rational exponent as a radical by extending the properties of integer exponents.

2 to the 3 over 4 power, all over 2 to the 1 over 2 power

the eighth root of 2 to the third power - THIS ONE
the square root of 2 to the 3 over 4 power
the fourth root of 2
the square root of 2

Answer 1

4th rout of 2

Explanation:

I did this quiz before

Answer 2

The answer is the fourth root of 2.

2 to the 3 over 4 power is
`2^{ (3)/(4) }`
2 to the 1 over 2 power is
`2^{ (1)/(2) }`
2 to the 3 over 4 power, all over 2 to the 1 over 2 power is
`\frac{2^{ (3)/(4) } }{2^{ (1)/(2) }}`

So, use the rule:
`(x^(a) )/( x^(b) ) = x^(a-b)`

`\frac{2^{ (3)/(4) } }{2^{ (1)/(2) }} = 2^{(3)/(4)- (1)/(2)}= 2^{(3)/(4)- (1*2)/(2*2)}= 2^{(3)/(4)- (2)/(4)}= 2^{ (3-2)/(4) } = 2^{ (1)/(4) }`

Now, use the rule:
`a^{ (m)/(n)} = \sqrt[n]{ x^(m) }`

`2^{ (1)/(4) } = \sqrt[4]{ 2^(1) }= \sqrt[4]{2}`
which is the same as the fourth root of 2.