Question

negative / zero exponents (level 1)
score: 1/4 penalty: none
question
which expression is equivalent to \\((5^6)^{-5}\\)?
answer
\\(\frac{1}{5^{12}}\\) \\(\frac{1}{5^{11}}\\)
5 \\(\frac{1}{5^{30}}\\)
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Explanation:

Step1: Apply exponent power rule

The power rule of exponents states that \((a^m)^n = a^{m\times n}\). For the expression \((5^6)^{-5}\), we multiply the exponents: \(6\times(-5)= - 30\). So, \((5^6)^{-5}=5^{-30}\).

Step2: Apply negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^n}\) (where \(a
eq0\) and \(n\) is an integer). For \(a = 5\) and \(n = 30\), we have \(5^{-30}=\frac{1}{5^{30}}\).

Answer:

\(\frac{1}{5^{30}}\) (assuming one of the options is \(\frac{1}{5^{30}}\), likely the option labeled \(\frac{1}{5^{30}}\) among the choices)