which expression is equivalent to 6^{-3}?\n-6^{3}\n3^{6}\nsqrt3{6}\n(\frac{1}{6})^{3}

which expression is equivalent to 6^{-3}?\n-6^{3}\n3^{6}\nsqrt3{6}\n(\frac{1}{6})^{3}

which expression is equivalent to 6^{-3}?\n-6^{3}\n3^{6}\nsqrt3{6}\n(\frac{1}{6})^{3}

Answer

Explanation:

Step1: Recall negative - exponent rule

According to the rule (a^{-n}=\frac{1}{a^{n}}), when (a = 6) and (n=3), we have (6^{-3}=\frac{1}{6^{3}}). And (\frac{1}{6^{3}}=(\frac{1}{6})^{3}).

Step2: Analyze each option

  • Option 1: (-6^{3}=- (6\times6\times6)= - 216), while (6^{-3}=\frac{1}{216}), so this option is incorrect.
  • Option 2: (3^{6}=3\times3\times3\times3\times3\times3 = 729), which is not equal to (6^{-3}), so this option is incorrect.
  • Option 3: (\sqrt[3]{6}=6^{\frac{1}{3}}), which is not equal to (6^{-3}), so this option is incorrect.
  • Option 4: ((\frac{1}{6})^{3}=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{216}), and (6^{-3}=\frac{1}{6^{3}}=\frac{1}{216}), so this option is correct.

Answer:

((\frac{1}{6})^{3})