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 negative - exponent rule

According to the rule $x^{-n}=\frac{1}{x^{n}}$, we have $(\frac{1}{4ab})^{-2}=(4ab)^{2}$.

Step2: Expand the square

Using the formula $(xy)^{n}=x^{n}y^{n}$, we get $(4ab)^{2}=4^{2}a^{2}b^{2}$.

Step3: Calculate $4^{2}$

Since $4^{2}=16$, then $4^{2}a^{2}b^{2}=16a^{2}b^{2}$.

Answer:

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