Simplify. Assume all variables are positive. u^(1/2)/(u^(5/2) * u^(1/2)) 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. u^(1/2)/(u^(5/2) * u^(1/2))   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

Write Expression: Write down the given expression. The expression is u^(1/2)/(u^(5/2) * u^(1/2)).Combine Denominator Exponents: Combine the exponents in the denominator using the property of exponents that states a^(m) * a^(n) = a^(m+n). u^(5/2) * u^(1/2) = u^(5/2 + 1/2) = u^(6/2) = u^3.Rewrite with Combined Denominator: Rewrite the expression with the combined denominator. The expression now is u^(1/2)/u^3.Simplify Using Exponent Property: Simplify the expression using the property of exponents that states a^(m)/a^(n) = a^(m-n). u^(1/2)/u^3 = u^(1/2 - 3) = u^(1/2 - 6/2) = u^(-5/2).Rewrite Negative Exponent: Since we want the exponent to be positive, we can rewrite u^(-5/2) as 1/u^(5/2). This is because a^(-n) = 1/a^n.Check Final Expression: Check the final expression to ensure it is in the form A or A/B with positive exponents. The final expression is 1/u^(5/2), which is in the form A/B with a positive exponent.

Full solution

More problems from Simplify expressions involving rational exponents

Related topics