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 11 let a and b be positive numbers. then ((ab)^x = a^{bx}). true false moving to another question will save this response.

Explanation:

Step1: Recall exponent rule

The power of a product rule states that \((ab)^x = a^x b^x\) for any real numbers \(a\), \(b\) (positive here) and \(x\).

Step2: Compare with given equation

The given equation is \((ab)^x = a^{b^x}\), which is not equivalent to \(a^x b^x\) in general. For example, let \(a = 2\), \(b = 3\), \(x = 2\). Then \((2\times3)^2=6^2 = 36\), and \(2^{3^2}=2^9 = 512\). Since \(36
eq512\), the statement is false.

Answer:

False