Simplify. Assume all variables are positive. x^(1/2)/(x^(5/2) * x^(3/2)) Write your answer in the form A or A/B, where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. ______

Question

Simplify.  Assume all variables are positive. x^(1/2)/(x^(5/2) * x^(3/2))   Write your answer in the form A or A/B, where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. ______

Bytelearn · Accepted Answer

Combine exponents in denominator: Combine the exponents in the denominator using the property of exponents that states when you multiply like bases, you add the exponents. x^(5/2) * x^(3/2) = x^(5/2 + 3/2)Add exponents in denominator: Add the exponents in the denominator. 5/2 + 3/2 = 8/2 8/2 = 4 So, x^(5/2) * x^(3/2) = x^4Rewrite with simplified denominator: Rewrite the original expression with the simplified denominator. x^(1/2) / (x^4)Apply division property of exponents: Apply the property of exponents that states when you divide like bases, you subtract the exponents. x^(1/2) / x^4 = x^(1/2 - 4)Convert whole number to fraction: Convert the whole number 4 into a fraction with the same denominator as 1/2 to subtract the exponents. 4 = 8/2 So, x^(1/2 - 4) = x^(1/2 - 8/2)Subtract exponents: Subtract the exponents. 1/2 - 8/2 = -7/2 So, x^(1/2 - 4) = x^(-7/2)Use property to make exponent positive: Since we want the exponent to be positive, we can use the property of exponents that states x^(-a) = 1/x^(a). x^(-7/2) = 1/x^(7/2)

Full solution

More problems from Simplify expressions involving rational exponents

Related topics