Simplify. Assume all variables are positive. d^(2/3)/(d^(8/3) * d^(8/3)) 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. ______

Write Expression: Write down the given expression. We have the expression d^(2/3) / (d^(8/3) * d^(8/3)).Combine Exponents: Combine the exponents in the denominator using the product rule for exponents. According to the product rule, when you multiply two powers with the same base, you add the exponents. So, d^(8/3) * d^(8/3) = d^(8/3 + 8/3) = d^(16/3).Rewrite with Combined Exponent: Rewrite the expression with the combined exponent in the denominator. Now the expression is d^(2/3) / d^(16/3).Simplify Using Quotient Rule: Simplify the expression using the quotient rule for exponents. According to the quotient rule, when you divide two powers with the same base, you subtract the exponents. So, d^(2/3) / d^(16/3) = d^(2/3 - 16/3) = d^(-14/3).Take Reciprocal for Positive Exponent: Since we want the exponent to be positive, we can rewrite the expression with a positive exponent by taking the reciprocal of the base. d^(-14/3) is the same as 1 / d^(14/3).Write Final Answer: Write the final answer in the form A or A/B with positive exponents. The final answer is 1 / d^(14/3).

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Simplify. Assume all variables are positive. $\newline$ $\frac{d^{\frac{2}{3}}}{d^{\frac{8}{3}} \cdot d^{\frac{8}{3}}}$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Simplify. Assume all variables are positive.

\newline

\frac{d^{\frac{2}{3}}}{d^{\frac{8}{3}} \cdot d^{\frac{8}{3}}}

\newline

Write your answer in the form

A

\frac{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.

\newline

______

Write Expression: Write down the given expression. $\newline$ We have the expression $d^{\frac{2}{3}} / (d^{\frac{8}{3}} * d^{\frac{8}{3}})$ .
Combine Exponents: Combine the exponents in the denominator using the product rule for exponents. $\newline$ According to the product rule, when you multiply two powers with the same base, you add the exponents. $\newline$ So, $d^{8/3} \times d^{8/3} = d^{8/3 + 8/3} = d^{16/3}.$
Rewrite with Combined Exponent: Rewrite the expression with the combined exponent in the denominator. $\newline$ Now the expression is $d^{\frac{2}{3}} / d^{\frac{16}{3}}$ .
Simplify Using Quotient Rule: Simplify the expression using the quotient rule for exponents. $\newline$ According to the quotient rule, when you divide two powers with the same base, you subtract the exponents. $\newline$ So, $d^{\frac{2}{3}} / d^{\frac{16}{3}} = d^{\frac{2}{3} - \frac{16}{3}} = d^{-\frac{14}{3}}$ .
Take Reciprocal for Positive Exponent: Since we want the exponent to be positive, we can rewrite the expression with a positive exponent by taking the reciprocal of the base. $\newline$ $d^{(-14/3)}$ is the same as $1 / d^{(14/3)}$ .
Write Final Answer: Write the final answer in the form $A$ or $A/B$ with positive exponents. $\newline$ The final answer is $\frac{1}{d^{\frac{14}{3}}}$ .