simplify the expression $\\left(\\frac{1}{4ab}\\right)^{-2}$. assume $a\\neq0,b\\neq0$.\n…

simplify the expression $\\left(\\frac{1}{4ab}\\right)^{-2}$. assume $a\\neq0,b\\neq0$.\n- $\\frac{1}{16a^{2}b^{2}}$\n- $\\frac{a^{2}b^{2}}{4}$\n- $-16a^{2}b^{2}$\n- $16a^{2}b^{2}$

simplify the expression $\\left(\\frac{1}{4ab}\\right)^{-2}$. assume $a\\neq0,b\\neq0$.\n- $\\frac{1}{16a^{2}b^{2}}$\n- $\\frac{a^{2}b^{2}}{4}$\n- $-16a^{2}b^{2}$\n- $16a^{2}b^{2}$

Answer

Explanation:

Step1: Apply power - of - a - quotient rule

$(\frac{1}{4ab})^{-2}=\frac{1^{-2}}{(4ab)^{-2}}$ Since $1^{-2} = 1$, the expression becomes $\frac{1}{(4ab)^{-2}}$.

Step2: Apply negative - exponent rule

$(4ab)^{-2}=\frac{1}{(4ab)^{2}}$ according to the rule $x^{-n}=\frac{1}{x^{n}}$. So $\frac{1}{(4ab)^{-2}}=(4ab)^{2}$.

Step3: Apply power - of - a - product rule

$(4ab)^{2}=4^{2}\times a^{2}\times b^{2}$ Since $4^{2}=16$, we have $16a^{2}b^{2}$.

Answer:

$16a^{2}b^{2}$