Question

question
use one exponent to condense the expression below. then compute and/or simplify.
$2ab \cdot 2ab \cdot 2ab \cdot 2ab \cdot 2ab$
answer attempt 1 out of 2
type the base, then use the $a^b$ button or type the ^ symbol on your keyboard for the exponent.
condensed form:
answer:

Explanation:

Step1: Identify the base and count

The expression is \(2ab \cdot 2ab \cdot 2ab \cdot 2ab \cdot 2ab\). The base being multiplied repeatedly is \(2ab\), and it is multiplied 5 times.

Step2: Apply exponent rule

Using the rule \(x \cdot x \cdot \dots \cdot x\) (n times) \(= x^n\), we can write \(2ab\) raised to the power of 5. So the condensed form is \((2ab)^5\).

Step3: Simplify the exponentiation

Now, expand \((2ab)^5\) using the power - of - a - product rule \((xyz)^n=x^n y^n z^n\). Here, \(x = 2\), \(y=a\), \(z = b\) and \(n = 5\).
We know that \(2^5=32\), \(a^5=a^5\) and \(b^5 = b^5\). So \((2ab)^5=2^5\times a^5\times b^5=32a^5b^5\)

Answer:

Condensed Form: \((2ab)^5\)