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Simplify. Express your answer using positive exponents. $\newline$ $\frac{4g^3}{2g \cdot g^7}$

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Multiply and divide powers: variable bases

Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

\frac{4g^3}{2g \cdot g^7}

Simplify Coefficients: Simplify the coefficients (numerical parts) of the expression. $\newline$ We have the coefficient $4$ in the numerator and $2$ in the denominator. We divide $4$ by $2$ to simplify. $\newline$ $4 / 2 = 2$
Apply Quotient Rule: Apply the quotient rule for the exponents of $g$ . The quotient rule states that when we divide powers with the same base, we subtract the exponents. $g^3 / (g \cdot g^7) = g^3 / g^8$ Now we subtract the exponents: $3 - 8 = -5$
Combine Results: Combine the results from Step $1$ and Step $2$ . $\newline$ We have the simplified coefficient of $2$ and the simplified exponent of $g$ which is $-5$ . $\newline$ So, the expression becomes $2 \times g^{-5}.$
Express with Positive Exponents: Express the answer using positive exponents. $\newline$ Since we have $g^{-5}$ , to express it with a positive exponent, we take the reciprocal of $g^5$ . $\newline$ $2 \times g^{-5} = \frac{2}{g^5}$

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