Question

1.Simplify ^3√-512

2.Simplify ^4√4096

3. Simplify (343) 1/3

4.Simplify ^6√x16

5. Solve. 2+^3√5x+2=10

Answer 1

`\text{Use:}\\\sqrt[n]{a^n}=a\\\\a^(m)/(n)=\sqrt[n]{a^m}\\\\(a^n)^m=a^(n\cdot m)\\\\a^n\cdot a^m=a^(n+m)\\\\1.\ \sqrt[3]{-512}=\sqrt[3]{(-8)^3}=-8\\\\2.\ \sqrt[4]{4096}=\sqrt[4]{8^4}=8\\\\3.\ 343^(1)/(3)=(7^3)^(1)/(3)=7^{3\cdot(1)/(3)}=7^1=7\\\\4.\ \sqrt[6]{x^(16)}=(x^(16))^(1)/(6)=x^{16\cdot(1)/(6)}=x^{8\cdot(1)/(3)}=x^(8)/(3)=x^{2(2)/(3)}=x^{2+(2)/(3)}=x^2x^(2)/(3)=x^2\sqrt[3]{x^2}`

`2+\sqrt[3]{5x+2}=10\ \ \ \ |-2\\\\\sqrt[3]{5x+2}=8\ \ \ \ |^3\\\\(\sqrt[3]{5x+2})^3=8^3\\\\5x+2=512\ \ \ \ |-2\\\\5x=510\ \ \ \ |:5\\\\x=102`