Simplify. Assume all variables are positive. s^(2/3)/(s^(4/3) * s^(4/3)) 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. ______

Apply Exponent Laws: Write down the expression and apply the laws of exponents for division and multiplication. We have the expression s^(2/3)/(s^(4/3) * s^(4/3)). According to the laws of exponents, when dividing powers with the same base, we subtract the exponents. When multiplying 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 s terms in the denominator. Since they have the same base, we add the exponents. s^(4/3) * s^(4/3) = s^(4/3 + 4/3) = s^(8/3) Now the expression is s^(2/3) / s^(8/3).Subtract Exponents: Subtract the exponents in the numerator and the denominator. Now we divide s^(2/3) by s^(8/3). Since they have the same base, we subtract the exponents. s^(2/3) / s^(8/3) = s^(2/3 - 8/3) = s^(-6/3)Simplify Exponent: Simplify the exponent. We can simplify the exponent -6/3 to -2. s^(-6/3) = s^(-2)Write Final Answer: Write the final answer with a positive exponent. Since we cannot have negative exponents in the final answer, we rewrite s^(-2) as 1/s^2.

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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{2}{3}}}{s^{\frac{4}{3}} \cdot s^{\frac{4}{3}}}$ $\newline$ 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{s^{\frac{2}{3}}}{s^{\frac{4}{3}} \cdot s^{\frac{4}{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

______

Apply Exponent Laws: Write down the expression and apply the laws of exponents for division and multiplication. $\newline$ We have the expression $s^{\frac{2}{3}}/(s^{\frac{4}{3}} \cdot s^{\frac{4}{3}})$ . According to the laws of exponents, when dividing powers with the same base, we subtract the exponents. When multiplying powers with the same base, we add the exponents.
Combine Exponents in Denominator: Combine the exponents in the denominator. $\newline$ First, we need to multiply the $s$ terms in the denominator. Since they have the same base, we add the exponents. $\newline$ $s^{4/3} \times s^{4/3} = s^{4/3 + 4/3} = s^{8/3}$ $\newline$ Now the expression is $s^{2/3} / s^{8/3}$ .
Subtract Exponents: Subtract the exponents in the numerator and the denominator. $\newline$ Now we divide $s^{2/3}$ by $s^{8/3}$ . Since they have the same base, we subtract the exponents. $\newline$ $s^{2/3} / s^{8/3} = s^{2/3 - 8/3} = s^{-6/3}$
Simplify Exponent: Simplify the exponent. $\newline$ We can simplify the exponent $-\frac{6}{3}$ to $-2$ . $\newline$ $s^{(-\frac{6}{3})} = s^{(-2)}$
Write Final Answer: Write the final answer with a positive exponent. $\newline$ Since we cannot have negative exponents in the final answer, we rewrite $s^{-2}$ as $1/s^2$ .