Question

1. select all expressions equivalent to 0.5 · 0.5 · 0.5. 0.5² × 0.5² 0.5³ 0.5² × 0.5¹ 3^0.5 0.5 × 3

Explanation:

Step1: Recall exponent rule

The product of the same number \(a\) multiplied \(n\) times is \(a^n\). Here \(0.5\cdot0.5\cdot0.5 = 0.5^3\).

Step2: Recall product - of - powers rule

The product - of - powers rule states that \(a^m\times a^n=a^{m + n}\). So \(0.5^2\times0.5^1=0.5^{2 + 1}=0.5^3\).

Step3: Analyze other options

For \(0.5^2\times0.5^2=0.5^{2 + 2}=0.5^4
eq0.5^3\), \(3^{0.5}=\sqrt{3}
eq0.5^3\), and \(0.5\times3 = 1.5
eq0.5^3\).

Answer:

\(0.5^3\), \(0.5^2\times0.5^1\)