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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}$ $\newline$ 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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Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{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

______

Identify given expression and rule: Identify the given expression and the rule for dividing powers with the same base. $\newline$ The expression is $(w^{4/3})/(w^{7/3})$ . According to the rules of exponents, when we divide two powers with the same base, we subtract the exponents: $a^m / a^n = a^{(m-n)}$ .
Subtract exponents of w: Subtract the exponents of w. $\newline$ We have $w^{\frac{4}{3}}$ divided by $w^{\frac{7}{3}}$ , so we subtract the exponents: $\left(\frac{4}{3}\right) - \left(\frac{7}{3}\right)$ .
Perform subtraction of exponents: Perform the subtraction of the exponents. $(\frac{4}{3}) - (\frac{7}{3}) = -\frac{3}{3}$ .
Simplify result of subtraction: Simplify the result of the subtraction. $-\frac{3}{3}$ simplifies to $-1$ .
Apply exponent to base $w$ : Apply the simplified exponent to the base $w$ . We now have $w^{-1}$ .
Write negative exponent as positive: Since the exponent is negative, we write it as a positive exponent in the denominator to satisfy the requirement that all exponents in the answer should be positive. $w^{-1}$ is equivalent to $\frac{1}{w^1}$ , which simplifies to $\frac{1}{w}$ .

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\newline

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5

\newline

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What is the probability of picking a number greater than

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