Question

simplify. express your answer using positive exponents.
$\frac{7g^{-1}}{7g^{4}}$

Explanation:

Step1: Simplify the coefficient

Since $\frac{7}{7}=1$, the expression becomes $\frac{g^{- 1}}{g^{4}}$.

Step2: Use exponent - rule for division

The rule for dividing terms with the same base $a^m\div a^n=a^{m - n}$. Here $a = g$, $m=-1$ and $n = 4$. So $\frac{g^{-1}}{g^{4}}=g^{-1-4}=g^{-5}$.

Step3: Convert to positive exponent

Using the rule $a^{-n}=\frac{1}{a^{n}}$, we get $g^{-5}=\frac{1}{g^{5}}$.

Answer:

$\frac{1}{g^{5}}$