I have a problem that I have no idea how to solve. The instruction say to solve and check the given equation by rational exponents. The equation is: x to the 5/2 power = 32. Can you show me how to do this step by step?
sure. x^5/2 is the square root of x^5.
So, you want x^5 = 32^2 = 2^10
x^5 = (2^2)^5
take the fifth root of both sides:
x = 2^2 = 4
So, the square root of 4 is 2
2^5 = 4^(5/2) = 32
Thanks Steve.
Of course! To solve the equation x^(5/2) = 32 using rational exponents, we need to find the value of x.
Step 1: Rewrite 32 as a power of 2: 32 = 2^5.
Step 2: Substitute this value back into the equation: x^(5/2) = 2^5.
Step 3: Apply the property of exponents which states that (a^m)^n = a^(m*n), to rewrite the equation as x^5/2 = (2^2)^5.
Step 4: Simplify both sides of the equation: x^5/2 = 2^10.
Step 5: Since the exponents have the same base, we can equate the exponents. Therefore, 5/2 = 10.
Step 6: Multiply both sides of the equation by 2 to get rid of the fraction: 5 = 20.
Step 7: This is a contradiction, as 5 does not equal 20. Therefore, there is no solution to the equation x^(5/2) = 32.
In summary, when solving the equation x^(5/2) = 32 using rational exponents, we found that there is no solution.