Find the solution(s) of the following equations.
x^4=21
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even.
- x= \sqrt[a]{b} if a is odd.
The problem x^4=21 is solved by taking the 4^{th} root of 21:
x^4=21
x=\pm \sqrt[4]{21}
The solutions are x=\pm \sqrt[4]{21}
x^2=16
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even
- x= \sqrt[a]{b} if a is odd
The problem x^2=16 is solved by taking the square root of 16:
x^2=16
x=\pm 4
The solutions are x=\pm 4.
x^3=27
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even
- x= \sqrt[a]{b} if a is odd
The problem x^3=27 is solved by taking the cube root of 27:
x^3=27
x= \sqrt[3]{27}
x=3
The solution is x=3.
x^9=15
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even
- x= \sqrt[a]{b} if a is odd
The problem x^9=15 is solved by taking the 9^{th} root of both sides:
x^9=15
x= \sqrt[9]{15}
The solution is x= \sqrt[9]{15}.
x^7=512
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even
- x= \sqrt[a]{b} if a is odd
The problem x^7=512 is solved by taking the 7^{th} root of 512:
x^7=512
x= \sqrt[7]{512}
The solution is x= \sqrt[7]{512}.
x^6=99
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even
- x= \sqrt[a]{b} if a is odd
The problem x^6=99 is solved by taking the 6^{th} root of 99:
x^6=99
x=\pm \sqrt[6]{99}
The solutions are x=\pm \sqrt[6]{99}.
x^7+15=200
Subtracting 15 from both sides gives:
x^7+15-15=200-15
x^7=185
Solving x^a=b requires taking the a^{th} root of b:
- x=\pm \sqrt[a]{b} if a is even
- x= \sqrt[a]{b} if a is odd
The problem x^7=185 is solved by taking the 7^{th} root of 185:
x^7=185
x= \sqrt[7]{185}
The solution is x= \sqrt[7]{185}.