SOLUTION: Please help me out with this one, "In this exercise, solve the equation containing a rational exponent on the variable." x^3/4= 125

Algebra ->  Rational-functions -> SOLUTION: Please help me out with this one, "In this exercise, solve the equation containing a rational exponent on the variable." x^3/4= 125      Log On


   

Question 554487: Please help me out with this one, "In this exercise, solve the equation containing a rational exponent on the variable."
x^3/4= 125
Found 2 solutions by ankor@dixie-net.com, bucky:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%283%2F4%29=+125
Find the cube root of both sides and you have
x%5E%281%2F4%29+=+125%5E%281%2F3%29
x%5E%281%2F4%29+=+5
Raise both sides to the 4 power
x = 5^4
x = 625

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given to solve for x:
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x%5E%283%2F4%29+=+125
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One way to solve this is to make use of the power rule of exponents. This rule says:
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%28x%5Ea%29%5Eb+=+x%5E%28a%2Ab%29
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Or in words ... if you have a base quantity with an exponent, and you raise it to a power, it is equal to the base quantity raised to product of the two exponents.
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So what would happen if we raised x%5E%283%2F4%29 to the 4%2F3 power. It would be equal to raising x to the exponent %283%2F4%29%2A%284%2F3%29. But in multiplying the two exponents you get 12%2F12+=+1. So raising x%5E%283%2F4%29 to the 4%2F3 power, it just becomes x%5E1 which is just x.
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However, if you raise one side of this equation to the 4%2F3 power, you must do the same to the other side to maintain the equality. In equation form this is now:
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x+=+125%5E%284%2F3%29
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The product rule means that we can interpret the exponent as the product of 4%2A%281%2F3%29 The right side of this equation can be interpreted in two ways. Either you can raise 125 to the 4th power and then take the cube root (the exponent 1/3 means cube root) of that answer. Or you can find the cube root (from the 1/3) of 125 and then raise that result to the 4th power.
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It's easier to do the second method. The cube root of 125 is 5. Then raise that to the 4th power to get 5*5*5*5 = 625. That's the answer to this problem:
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x+=+625
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Hope this helps you in your understanding of exponents.