Question

test information description instructions multiple attempts this test allows multiple attempts. force completion this test can be saved and resumed later. your answers are saved automatically. question completion status: moving to another question will save this response. question 5 (3^a^b = 3^{ab}) true false moving to another question will save this response.

Explanation:

Step1: Recall exponent rule

The power - of - a - power rule states that \((x^{m})^{n}=x^{m\times n}\) for any real number \(x\) and integers \(m\) and \(n\) (this rule also holds for real number exponents in the context of exponential functions with base \(x>0\)).

Step2: Apply the rule to the given expression

For the expression \((3^{a})^{b}\), using the power - of - a - power rule, where \(x = 3\), \(m=a\) and \(n = b\), we have \((3^{a})^{b}=3^{a\times b}=3^{ab}\).

Answer:

True