Question

4 from unit 4, lesson 3
suppose that a friend missed class and never learned what ( 37^{\frac{1}{3}} ) means.
a. use exponent rules that your friend would already know to show your friend how to calculate ( left(37^{\frac{1}{3}}
ight)^{3} ).

Explanation:

Step1: Apply the power - of - a - power rule

The power - of - a - power rule states that \((a^{m})^{n}=a^{mn}\). For \((37^{\frac{1}{3}})^{3}\), where \(a = 37\), \(m=\frac{1}{3}\), and \(n = 3\).

$$ (37^{\frac{1}{3}})^{3}=37^{\frac{1}{3}\times3} $$

Step2: Simplify the exponent

Calculate \(\frac{1}{3}\times3\).

$$ \frac{1}{3}\times3 = 1 $$

So, \(37^{\frac{1}{3}\times3}=37^{1}\)

Step3: Evaluate the expression

Since \(a^{1}=a\) for any non - zero real number \(a\), when \(a = 37\), \(37^{1}=37\)

Answer:

\(37\)