Question

Radicals and Exponents Indicate whether the statement is true or false

Answer 1

1.

`\begin{gathered} \sqrt[m]{a^n}=a^{(n)/(m)}^{} \\ \text{and} \\ (\sqrt[m]{a})^n=(a^{(1)/(m)})^n=a^{(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[]{(3)/(5)}\text{ is simplified}`

Answer 3: true

4.

`a^x+b^x\\e(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}=(-c)/(a)\text{ } \\ \sqrt[3]{x+b}=-(c)/(a)\text{ (isolate }\sqrt[3]{x+b}) \end{gathered}`

Answer 5: true