Question

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I can’t get this ! Please help

Answer 1

`√(2^5)`

Explanation:

First, deal with the product of the two powers of 2 inside the parentheses.

The two factors are powers of 2, so add the exponents.

`(2^{(1)/(2)} \cdot 2^{(3)/(4)})^2 =`

`= (2^{(1)/(2) + (3)/(4)})^2`

You need a common denominator, 4, to add the fractions.

`= (2^{(2)/(4) + (3)/(4)})^2`

`= (2^{(5)/(4)})^2`

Now you have an exponent raised to an exponent. Multiply the exponents and reduce the fraction.

`= 2^{(5)/(4) * 2}`

`= 2^{(10)/(4)}`

`= 2^{(5)/(2)}`

When a fraction is an exponent, the numerator is an exponent and the denominator is the index of the root. A denominator of 2 means a root index of 2 which means square root.

`= √(2^5)`