Question

name
date
cool down
lesson 12: meaning of exponents
cool down: more 3s
$3^5$ equals 243. explain how to use that fact to quickly evaluate $3^6$.

Explanation:

Step1: Recall exponent rule

The exponent rule for multiplication: \(a^m \times a^n = a^{m + n}\). So, \(3^6\) can be written as \(3^{5+1}\).

Step2: Apply the rule

Using the rule \(a^{m + n}=a^m\times a^n\), we have \(3^{5 + 1}=3^5\times3^1\).

Step3: Substitute known value

We know that \(3^5 = 243\) and \(3^1=3\). So, \(3^5\times3^1 = 243\times3\).

Step4: Calculate the product

\(243\times3 = 729\).

Answer:

To evaluate \(3^6\) using \(3^5 = 243\), we use the exponent rule \(a^{m + n}=a^m\times a^n\). Rewrite \(3^6\) as \(3^{5+1}=3^5\times3^1\). Substitute \(3^5 = 243\) and \(3^1 = 3\), then multiply: \(243\times3 = 729\). So \(3^6 = 729\).