Simplify. Assume all variables are positive. v^(2/3)/(v^(7/3) * v^(5/3)) 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. ______

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Simplify.  Assume all variables are positive. v^(2/3)/(v^(7/3) * v^(5/3))   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. v^(7/3) * v^(5/3) = v^(7/3 + 5/3)Add Exponents: Add the exponents in the denominator. 7/3 + 5/3 = 12/3 v^(7/3 + 5/3) = v^(12/3)Simplify Exponent: Simplify the exponent in the denominator. 12/3 = 4 v^(12/3) = v^4Rewrite Expression: Rewrite the original expression with the simplified denominator. v^(2/3) / (v^4)Apply Exponent Property: Apply the property of exponents that states when you divide like bases, you subtract the exponents. v^(2/3) / v^4 = v^(2/3 - 4)Convert Whole Number: Convert the whole number 4 to a fraction with the same denominator as 2/3 to subtract the exponents. 4 = 12/3 v^(2/3 - 4) = v^(2/3 - 12/3)Subtract Exponents: Subtract the exponents. 2/3 - 12/3 = -10/3 v^(2/3 - 12/3) = v^(-10/3)Use Negative Exponent Property: Since we want the exponent to be positive, we can use the property of exponents that states a negative exponent means the reciprocal of the base raised to the positive exponent. v^(-10/3) = 1/v^(10/3)

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