which expression is equivalent to $\\left(\\frac{1}{16}\\right)^{-4}$?\n-$(16)^{4}$\n$16^{4}$\n$\\sqrt4{\\fra…

which expression is equivalent to $\\left(\\frac{1}{16}\\right)^{-4}$?\n-$(16)^{4}$\n$16^{4}$\n$\\sqrt4{\\frac{1}{16}}$\n-$\\left(\\frac{1}{16}\\right)^{-4}$

which expression is equivalent to $\\left(\\frac{1}{16}\\right)^{-4}$?\n-$(16)^{4}$\n$16^{4}$\n$\\sqrt4{\\frac{1}{16}}$\n-$\\left(\\frac{1}{16}\\right)^{-4}$

Answer

Explanation:

Step1: Apply negative - exponent rule

The negative - exponent rule states that $a^{-n}=\frac{1}{a^{n}}$ and $\left(\frac{1}{a}\right)^{-n}=a^{n}$. For the expression $\left(\frac{1}{16}\right)^{-4}$, using the rule $\left(\frac{1}{a}\right)^{-n}=a^{n}$, where $a = 16$ and $n = 4$, we get $\left(\frac{1}{16}\right)^{-4}=16^{4}$.

Step2: Analyze other options

  • Option 1: $-(16)^{4}$ is the negative of $16^{4}$, so it is not equivalent.
  • Option 3: $\sqrt[4]{\frac{1}{16}}=\left(\frac{1}{16}\right)^{\frac{1}{4}}=\frac{1}{2}$, which is not equivalent.
  • Option 4: $-\left(\frac{1}{16}\right)^{-4}$ is the negative of $\left(\frac{1}{16}\right)^{-4}$, so it is not equivalent.

Answer:

$16^{4}$