Full solution

Q. Simplify. Express your answer using positive exponents.

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\frac{7w}{w^7 \cdot 7w}

Write Expression, Identify Terms: Write down the expression and identify like terms. $\newline$ The expression given is $\frac{7w}{w^7 \cdot 7w}$ . We can see that there are like terms in the numerator and the denominator that can be simplified.
Simplify Coefficients: Simplify the coefficients. $\newline$ The coefficients $7$ in the numerator and $7$ in the denominator can be simplified because they are the same number. $\newline$ $\frac{7w}{w^7 \cdot 7w} = \frac{w}{w^7 \cdot w}$
Simplify Variables with Exponents: Simplify the variables with exponents. $\newline$ We have $w$ in the numerator and $w^7 \times w$ in the denominator. When dividing powers with the same base, we subtract the exponents. $\newline$ $\frac{w}{w^7 \times w} = \frac{w}{w^{7+1}} = \frac{w}{w^8}$
Subtract Exponents: Subtract the exponents. $\newline$ Now we subtract the exponents of $w$ in the numerator from the exponents of $w$ in the denominator. $\newline$ $\frac{w}{w^8} = w^{1-8} = w^{-7}$
Express Answer with Positive Exponents: Express the answer with positive exponents. $\newline$ Since we want the answer with positive exponents, we can write $w^{-7}$ as $1/w^7$ . $\newline$ $w^{-7} = 1/w^7$