Question

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

Answer 1

Answer:

See explanation

Step-by-step explanation:

1. To rewrite the expression

$(4^{\frac{2}{5}})^{\frac{1}{4}},$

use exponents property

$(a^m)^n=a^{m\cdot n}$

So,

$(4^{\frac{2}{5}})^{\frac{1}{4}}=4^{\frac{2}{5}\cdot \frac{1}{4}}=4^{\frac{2}{20}}=4^{\frac{1}{10}}$

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

Raise both sides to 10 power:

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

So,

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

3. Simplify $\dfrac{3^4}{9}$

Use  the Quotient of Powers Property:

$\dfrac{a^m}{a^n}=a^{m-n}$

Then

$\dfrac{3^4}{9}=\dfrac{3^4}{3^2}=3^{4-2}=3^2$

4. Solve $4\sqrt{2}+5\sqrt{4}$

First, note that $\sqrt{4}=2,$ then

$4\sqrt{2}+5\sqrt{4}=4\sqrt{2}+5\cdot 2=4\sqrt{2}+10$

Number $4\sqrt{2}$ is irrational number, number 10 is rational number. The sum of irrational and rational numbers is irrational number.

5. The same as option 4.