which shows the following expression after the negative exponents have been eliminated?\n$\frac{a^{3}b^{-2}}{…

which shows the following expression after the negative exponents have been eliminated?\n$\frac{a^{3}b^{-2}}{ab^{-4}},a\neq0,b\neq0$\n$\frac{a^{3}b^{-4}}{ab^{-2}}$\n$\frac{ab^{4}}{a^{3}b^{2}}$\n$-\frac{a^{3}b^{4}}{ab^{2}}$\n$\frac{a^{3}b^{4}}{ab^{2}}$

which shows the following expression after the negative exponents have been eliminated?\n$\frac{a^{3}b^{-2}}{ab^{-4}},a\neq0,b\neq0$\n$\frac{a^{3}b^{-4}}{ab^{-2}}$\n$\frac{ab^{4}}{a^{3}b^{2}}$\n$-\frac{a^{3}b^{4}}{ab^{2}}$\n$\frac{a^{3}b^{4}}{ab^{2}}$

Answer

Explanation:

Step1: Use negative - exponent rule

Recall that $x^{-n}=\frac{1}{x^{n}}$ and $\frac{1}{x^{-n}} = x^{n}$. For the given expression $\frac{a^{3}b^{-2}}{ab^{-4}}$, we can rewrite it as $a^{3}\times\frac{1}{b^{2}}\times\frac{1}{a}\times b^{4}$.

Step2: Simplify the coefficients and variables

First, simplify the $a$ - terms: $\frac{a^{3}}{a}=a^{3 - 1}=a^{2}$ (using the rule $\frac{x^{m}}{x^{n}}=x^{m - n}$). Then, simplify the $b$ - terms: $\frac{b^{4}}{b^{2}}=b^{4-2}=b^{2}$ (using the same rule). So, $\frac{a^{3}b^{-2}}{ab^{-4}}=\frac{a^{3}b^{4}}{ab^{2}}$.

Answer:

$\frac{a^{3}b^{4}}{ab^{2}}$