Question

cphs : advanced algebra: concepts and connections - block (27.0831030)
negative exponents
reviewing laws of exponents
write the expression using a single exponent.
\\(\left(6^{2}\
ight)^{7}\\)
\\(6^{49}\\) \\(6^{5}\\) \\(6^{9}\\) \\(6^{14}\\)

Explanation:

Step1: Recall exponent power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\).

Step2: Apply the rule to \((6^2)^7\)

Here, \(a = 6\), \(m = 2\), and \(n = 7\). So we calculate \(2\times7 = 14\). Thus, \((6^2)^7 = 6^{14}\).

Answer:

\(6^{14}\)