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Simplify. Express your answer using positive exponents. $\newline$ $\frac{2v^2}{2v^7}$

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Multiply and divide powers: variable bases

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Q. Simplify. Express your answer using positive exponents.

\newline

\frac{2v^2}{2v^7}

Simplify Coefficients and Apply Quotient Rule: Simplify the coefficients and apply the quotient rule for exponents. $\newline$ The quotient rule for exponents states that when we divide two powers with the same base, we subtract the exponents. First, we simplify the coefficients (the numbers in front of the variables). $\newline$ $\frac{2}{2} = 1$ $\newline$ Now we apply the quotient rule to the exponents of $v$ . $\newline$ $\frac{v^2}{v^7} = v^{2-7}$
Calculate Exponent After Quotient Rule: Calculate the exponent after applying the quotient rule. $\newline$ $v^{2-7} = v^{-5}$ $\newline$ Since we want to express the answer using positive exponents, we need to rewrite the negative exponent as a positive exponent. $\newline$ $v^{-5} = \frac{1}{v^5}$
Combine Results: Combine the results from Step $1$ and Step $2$ . $\newline$ Since the coefficient simplifies to $1$ , we are left with the variable part. $\newline$ $1 \times (1/v^5) = 1/v^5$

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