Question

I need help with this, neither of my parents can help me and i want to understand.

1- Rewrite the expression with a rational exponent as a radical expression.


four to the two fifths power all raised the one fourth power

2- Which equation justifies why ten to the one third power equals the cube root of ten?

3-
Explain how the Quotient of Powers Property was used to simplify this expression.

three to the fourth power all over nine equals three squared

4-
Solve four square root of two plus five square root of four and explain whether the answer is rational or irrational.

5-
Solve four square root of two plus five square root of four and explain whether the answer is rational or irrational.

Answer 1

See explanation

Explanation:

1. To rewrite the expression

`(4^{(2)/(5)})^{(1)/(4)},`

use exponents property

`(a^m)^n=a^(m\cdot n)`

So,

`(4^{(2)/(5)})^{(1)/(4)}=4^{(2)/(5)\cdot (1)/(4)}=4^{(2)/(20)}=4^{(1)/(10)}`

2. Why
`10^{(1)/(3)}=\sqrt[3]{10}?`

Raise both sides to 10 power:

`(10^{(1)/(3)})^3=10^{(1)/(3)\cdot 3}=10^1=10\\ \\(\sqrt[3]{10})^3=10`

So,

`(10^{(1)/(3)})^3=(\sqrt[3]{10} )^3`

3. Simplify
`(3^4)/(9)`

Use the Quotient of Powers Property:

`(a^m)/(a^n)=a^(m-n)`

Then

`(3^4)/(9)=(3^4)/(3^2)=3^(4-2)=3^2`

4. Solve
`4√(2)+5√(4)`

First, note that
`√(4)=2,` then

`4√(2)+5√(4)=4√(2)+5\cdot 2=4√(2)+10`

Number
`4√(2)` is irrational number, number 10 is rational number. The sum of irrational and rational numbers is irrational number.

5. The same as option 4.