Simplify. Assume all variables are positive. d^(4/3)/(d^(2/3) * d^(7/3)) 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. d^(4/3)/(d^(2/3) * d^(7/3))   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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Write and apply properties: Write down the expression and apply the properties of exponents. We have the expression d^(4/3)/(d^(2/3) * d^(7/3)). According to the properties of exponents, when we divide powers with the same base, we subtract the exponents. When we multiply powers with the same base, we add the exponents.Combine exponents in denominator: Combine the exponents in the denominator. First, we need to multiply the terms in the denominator. Since they have the same base, we add the exponents. d^(2/3) * d^(7/3) = d^(2/3 + 7/3) = d^(9/3)Simplify denominator: Simplify the denominator. Now that we have combined the exponents, we can simplify the denominator. d^(9/3) = d^3Divide terms with same base: Divide the terms with the same base. Now we divide the term in the numerator by the term in the denominator. d^(4/3) / d^3 According to the properties of exponents, we subtract the exponents. d^(4/3 - 3)Convert whole number exponent: Convert the whole number exponent to a fraction. To subtract the exponents, we need to express the whole number exponent as a fraction with the same denominator. 3 = 9/3 So, d^(4/3 - 9/3)Subtract exponents: Subtract the exponents. Now we subtract the exponents to simplify the expression. d^(4/3 - 9/3) = d^(-5/3)Express answer with positive exponent: Express the answer with a positive exponent. Since the problem asks for positive exponents, we need to rewrite the expression with a positive exponent. A negative exponent means the reciprocal of the base raised to the positive exponent. d^(-5/3) = 1/d^(5/3)

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