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question 5
let a and b be positive numbers. then ((ab)^b = a^{b^2}).
○ true
○ false
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Explanation:

Step1: Recall exponent rules

The power of a product rule states that \((xy)^n = x^n y^n\) for any real numbers \(x\), \(y\) and positive integer \(n\) (or real number \(n\) when \(x,y>0\)). So \((ab)^b=a^b b^b\), not \(a^{b^2}\).

Step2: Analyze the given equation

The given equation is \((ab)^b = a^{b^2}\). From the power of a product rule, the left - hand side expands to \(a^b b^b\), which is not equal to \(a^{b^2}\) in general (for example, let \(a = 2\), \(b = 3\). Then \((2\times3)^3=6^3 = 216\), and \(2^{3^2}=2^9 = 512\), and \(216
eq512\)).

Answer:

False