Question

2 write an expression equivalent to 100^n.

Explanation:

Step1: Recall exponent rules

We know that \(100 = 10^2\), so we can rewrite \(100^n\) using the power - of - a - power rule \((a^m)^n=a^{m\times n}\).

Step2: Apply the power - of - a - power rule

Substitute \(a = 10\) and \(m = 2\) into the power - of - a - power rule. So \((10^2)^n=10^{2n}\). Also, we know that \(100 = 2^2\times5^2\), so another equivalent expression could be \((2^2\times5^2)^n=2^{2n}\times5^{2n}\) (using the power of a product rule \((ab)^n=a^n\times b^n\)). But a simple and common equivalent expression is using base 10. So \(100^n=(10^2)^n = 10^{2n}\) or also \(100^n=(2\times50)^n\), but the most straightforward one using the power - of - a - power rule is \(10^{2n}\) or we can also note that \(100 = 10\times10\), so \(100^n=(10\times10)^n=10^n\times10^n = 10^{n + n}=10^{2n}\) (using the product of powers rule \(a^m\times a^n=a^{m + n}\)).

Answer:

One equivalent expression is \(10^{2n}\) (other equivalent expressions like \(2^{2n}\times5^{2n}\) or \((10\times10)^n\) are also correct).