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Simplify. Assume all variables are positive.Write your answer in the form or , where and are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.______
Full solution
Q. Simplify. Assume all variables are positive.Write your answer in the form or , where and are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.______
- Combine Exponents in Denominator: We start by looking at the expression . To simplify, we can use the properties of exponents to combine the exponents in the denominator.
- Simplify Denominator: Using the property of exponents that states , we combine the exponents in the denominator:
- Rewrite Expression: Now we rewrite the original expression with the simplified denominator: .
- Use Exponent Property: Next, we use the property of exponents that states to simplify the expression further:$c^{(\(5\)/\(2\))} / c^{\(4\)} = c^{((\(5\)/\(2\)) - \(4\))} = c^{((\(5\)/\(2\)) - (\(8\)/\(2\)))} = c^{(\(-3\)/\(2\))}.
- Express with Positive Exponents: Since we are asked to write the answer with positive exponents and without variables in common in the numerator and denominator, we can express \(c^{(-3/2)}\) as \(1/c^{(3/2)}\).
- Final Simplified Expression: The final simplified expression is \(\frac{1}{c^{\frac{3}{2}}}\). This is the simplest form of the expression with positive exponents and no variables in common in the numerator and denominator.
