Question

14.
Simplify the expression.

(x9)0(x7)2


1


x14


x126


x18

Answer 1

To simplify the expression \((x^9)^0 (x^7)^2\), let's break it down step-by-step:

1. First, apply the zero exponent rule which states that any non-zero number raised to the power of 0 is 1:
\[
(x^9)^0 = 1
\]

Thus, the expression now looks like this:
\[
1 \cdot (x^7)^2
\]

2. Next, simplify \((x^7)^2\) using the power of a power rule which states that \((a^m)^n = a^{m \cdot n}\):
\[
(x^7)^2 = x^{7 \cdot 2} = x^{14}
\]

3. Now, multiply the results:
\[
1 \cdot x^{14} = x^{14}
\]

So, the simplified expression is:
\[
x^{14}
\]

Therefore, the correct answer is:
\[
\boxed{x^{14}}
\]