Question

Question 1: Rewrite the rational exponent as a radical:

5 to the 3 over 4 power, to the 2 over 3 power

A.) the cube root of 5 squared.
B.) the twelfth root of 5.
C.) the square root of 5.
D.) the cube root of 5 the fourth power.

Question 2: Explain how the Quotient of Powers was used to simplify this expression:
5 to the fourth power, over 25 = 52

A.) By simplifying 25 to 52 to make both powers base five, and subtracting the exponents.
B.) By simplifying 25 to 52 to make both powers base five, and adding the exponents.
C.) By finding the quotient of the bases to be,

Answer 1

1.C.The square root of 5

2.A.by simplifying 25 to
`5^2` to make both powers base five, and subtracting the exponents.

Explanation:

1.We are given that

`((5)^{(3)/(4)})^{(2)/(3)`

We have to rewrite the rational exponent as a radical.

Radical expression includes square root, cube root, fourth root etc.

`(5)^(3)/(4)* (2)/(3)`

By using the property
`(a^x)^y=a^(xy)`

`(5)^{(1)/(2)}=\sqrt5`

Hence, option C is correct.

2.We are given that

`(5^4)/(25)`

The expression can be write as

`(5^4)/(5^2)`

We know that
`(a^x)/(a^y)=a^(x-y)`

Using the property

`5^(4-2)=5^2`

Hence, the option A is true.

Answer: A. By simplifying 25 to
`5^2` to make both powers base five , and subtracting the exponents.

Answer 2

Question 1 is expressed from the given statement the expression (5^(3/4))^(2/3). In this case, we multiply the powers of 5 whih is equal to 1/2. Hence the expression is simplified to 5^1/2, C.Question 2. The statement is represented by (5^4) /25. We take the fourth power of 5 first equal to 625 and divide by 25, equal to 52