5.3k views
15 votes
Help
I can’t get this ! Please help

Help I can’t get this ! Please help-example-1
User TNR
by
8.2k points

1 Answer

8 votes

Answer:


√(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)

User Ihor Dobrovolskyi
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories