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.

Question

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Respuesta :

frika frika · Answer 1 · 2019-10-10T22:56:49+02:00

Answer:

See explanation

Step-by-step explanation:

1. To rewrite the expression

[tex](4^{\frac{2}{5}})^{\frac{1}{4}},[/tex]

use exponents property

[tex](a^m)^n=a^{m\cdot n}[/tex]

So,

[tex](4^{\frac{2}{5}})^{\frac{1}{4}}=4^{\frac{2}{5}\cdot \frac{1}{4}}=4^{\frac{2}{20}}=4^{\frac{1}{10}}[/tex]

2. Why [tex]10^{\frac{1}{3}}=\sqrt[3]{10}?[/tex]

Raise both sides to 10 power:

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

So,

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

3. Simplify [tex]\dfrac{3^4}{9}[/tex]

Use the Quotient of Powers Property:

[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]

Then

[tex]\dfrac{3^4}{9}=\dfrac{3^4}{3^2}=3^{4-2}=3^2[/tex]

4. Solve [tex]4\sqrt{2}+5\sqrt{4}[/tex]

First, note that [tex]\sqrt{4}=2,[/tex] then

[tex]4\sqrt{2}+5\sqrt{4}=4\sqrt{2}+5\cdot 2=4\sqrt{2}+10[/tex]

Number [tex]4\sqrt{2}[/tex] is irrational number, number 10 is rational number. The sum of irrational and rational numbers is irrational number.

5. The same as option 4.