Question

which expression is equivalent to (left(m^{1.5}
ight)^{1.5})?
a. (m^{2.25})
b. (m^{4.5})
c. (m^{3.25})
d. (m^{1.5})

Explanation:

Step1: Recall the power of a power rule

The power of a power rule states that \((a^m)^n = a^{m \times n}\). Here, \(a = m\), \(m = 1.5\), and \(n = 1.5\).

Step2: Apply the power of a power rule

We have \((m^{1.5})^{1.5}\). Using the power of a power rule, we multiply the exponents: \(1.5\times1.5 = 2.25\). So, \((m^{1.5})^{1.5}=m^{2.25}\).

Answer:

A. \(m^{2.25}\)