marina correctly simplified the expression $\frac{-4a^{-2}b^{4}}{8a^{-6}b^{-3}}$, assuming that $a\neq0$ and…

marina correctly simplified the expression $\frac{-4a^{-2}b^{4}}{8a^{-6}b^{-3}}$, assuming that $a\neq0$ and $b\neq0$. her simplified expression is below. \n$-\frac{1}{2}a^{4}b^{square}$\nwhat exponent should marina use for $b$?\n-7\n-1\n1\n7

marina correctly simplified the expression $\frac{-4a^{-2}b^{4}}{8a^{-6}b^{-3}}$, assuming that $a\neq0$ and $b\neq0$. her simplified expression is below. \n$-\frac{1}{2}a^{4}b^{square}$\nwhat exponent should marina use for $b$?\n-7\n-1\n1\n7

Answer

Explanation:

Step1: Simplify the coefficient

$\frac{-4}{8}=-\frac{1}{2}$

Step2: Simplify the $a$ - terms using exponent rule $\frac{a^m}{a^n}=a^{m - n}$

$\frac{a^{-2}}{a^{-6}}=a^{-2-(-6)}=a^{-2 + 6}=a^{4}$

Step3: Simplify the $b$ - terms using exponent rule $\frac{b^m}{b^n}=b^{m - n}$

$\frac{b^{4}}{b^{-3}}=b^{4-(-3)}=b^{4 + 3}=b^{7}$

Answer:

D. 7