Question

simplify. express your answer as a single term using exponents.\\(\frac{314^{2}}{314^{9}}\\)

Explanation:

Step1: Recall exponent rule for division

When dividing two terms with the same base, we subtract the exponents: $\frac{a^m}{a^n} = a^{m - n}$ (where $a
eq 0$). Here, the base $a = 314$, $m = 2$, and $n = 9$.

Step2: Apply the exponent rule

Substitute the values into the formula: $314^{2 - 9}$.

Step3: Calculate the exponent

Simplify the exponent: $2 - 9 = -7$. So we get $314^{-7}$.

Answer:

$314^{-7}$