Question

Radicals and Exponents Indicate whether the statement is true or false

Answer 1

1.

$\begin{gathered} \sqrt[m]{a^n}=a^{\frac{n}{m}}^{} \\ \text{and} \\ (\sqrt[m]{a})^n=(a^{\frac{1}{m}})^n=a^{\frac{n}{m}} \end{gathered}$

Answer 1: true

2.

$\sqrt[]{-a^3b}\sqrt[]{-ab^3}=\sqrt[]{-a^3b\cdot-ab^3}=\sqrt[]{a^4b^4}=a^2b^2$

Answer 2: true

3.

$\sqrt[]{\frac{3}{5}}\text{ is simplified}$

Answer 3: true

4.

$a^x+b^x\ne(a+b)^x$

Answer 4: false

5.

$\begin{gathered} a\sqrt[3]{x+b}+c=0 \\ subtract\text{ c} \\ a\sqrt[3]{x+b}+c-c=0-c \\ a\sqrt[3]{x+b}=-c \\ \text{divide by a} \\ \frac{a\sqrt[3]{x+b}}{a}=\frac{-c}{a}\text{ } \\ \sqrt[3]{x+b}=-\frac{c}{a}\text{ (isolate }\sqrt[3]{x+b}) \end{gathered}$

Answer 5: true