Simplify. Assume all variables are positive. z^(1/2)/(z^(1/2) * z^(3/2)) 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 expression. We have the expression z^(1/2)/(z^(1/2) * z^(3/2)).Apply Exponent Property: Apply the property of exponents for multiplication. When multiplying powers with the same base, we add the exponents. z^(1/2) * z^(3/2) = z^(1/2 + 3/2) = z^(4/2) = z^2.Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator. Now the expression is z^(1/2)/z^2.Apply Exponent Property for Division: Apply the property of exponents for division. When dividing powers with the same base, we subtract the exponents. z^(1/2)/z^2 = z^(1/2 - 2/1) = z^(1/2 - 4/2) = z^(-3/2).Write Final Answer: Write the final answer with positive exponents. Since we cannot have negative exponents in the final answer, we rewrite z^(-3/2) as 1/z^(3/2).

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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{1}{2}}}{z^{\frac{1}{2}} \cdot z^{\frac{3}{2}}}$ $\newline$ 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{z^{\frac{1}{2}}}{z^{\frac{1}{2}} \cdot z^{\frac{3}{2}}}

\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 expression. $\newline$ We have the expression $\frac{z^{\frac{1}{2}}}{z^{\frac{1}{2}} \cdot z^{\frac{3}{2}}}$ .
Apply Exponent Property: Apply the property of exponents for multiplication. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $z^{\frac{1}{2}} \times z^{\frac{3}{2}} = z^{\frac{1}{2} + \frac{3}{2}} = z^{\frac{4}{2}} = z^2$ .
Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator. $\newline$ Now the expression is $z^{\frac{1}{2}}/z^2$ .
Apply Exponent Property for Division: Apply the property of exponents for division. When dividing powers with the same base, we subtract the exponents. $z^{1/2}/z^2 = z^{1/2 - 2/1} = z^{1/2 - 4/2} = z^{-3/2}.$
Write Final Answer: Write the final answer with positive exponents. $\newline$ Since we cannot have negative exponents in the final answer, we rewrite $z^{(-3/2)}$ as $1/z^{(3/2)}$ .