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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{13}{7}}}{w^{\frac{12}{7}}}$ $\newline$ 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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Simplify expressions involving rational exponents I

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{13}{7}}}{w^{\frac{12}{7}}}

\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

______

Rewrite using Quotient Rule: Given expression: $w^{\frac{13}{7}}/w^{\frac{12}{7}}$ $\newline$ Rewrite this expression as a single power of $w$ using the quotient rule for exponents, which states that $a^m / a^n = a^{m-n}$ . $\newline$ $w^{\frac{13}{7}}/w^{\frac{12}{7}} = w^{\frac{13}{7} - \frac{12}{7}}$
Simplify Exponent: Simplify the exponent in $w^{\frac{13}{7} - \frac{12}{7}}$ $\newline$ Subtract the exponents: $\frac{13}{7} - \frac{12}{7} = \frac{1}{7}$ $\newline$ $w^{\frac{13}{7} - \frac{12}{7}} = w^{\frac{1}{7}}$
Ensure Positive Exponent: Ensure the exponent is positive. The exponent $\frac{1}{7}$ is already positive, so no further action is needed. $w^{\frac{1}{7}}$ is the simplified expression with a positive exponent.

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