Question

which of the following is equivalent to ( 60^{-\frac{1}{2}} )? (\frac{1}{sqrt{60}}) (sqrt{60}) (\frac{60}{2}) (\frac{1}{60^2}) (\frac{1}{sqrt{60}})

Explanation:

Step1: Recall exponent rule

The negative exponent rule: \(a^{-n}=\frac{1}{a^{n}}\), and the fractional exponent rule: \(a^{\frac{1}{n}}=\sqrt[n]{a}\). For \(60^{-\frac{1}{2}}\), we can split the exponents. First, using the negative exponent rule: \(60^{-\frac{1}{2}}=\frac{1}{60^{\frac{1}{2}}}\).

Step2: Apply fractional exponent

Then, using the fractional exponent rule on \(60^{\frac{1}{2}}\), we know that \(60^{\frac{1}{2}} = \sqrt{60}\). So \(\frac{1}{60^{\frac{1}{2}}}=\frac{1}{\sqrt{60}}\).

Step3: Check other options

• For \(\frac{60}{2}\), it is just \(30\), not related to \(60^{-\frac{1}{2}}\).
• For \(\frac{1}{60^{2}}\), it is \(60^{-2}\), not \(60^{-\frac{1}{2}}\).
• For \(\sqrt{60}\), it is \(60^{\frac{1}{2}}\), not the negative version.

Answer:

\(\frac{1}{\sqrt{60}}\) (the option with \(\frac{1}{\sqrt{60}}\))