Question

simplify. express your answer using positive exponents.\\(\frac{w^{-3}}{w^{4}}\\)

Explanation:

Step1: Apply exponent subtraction rule

When dividing like bases, subtract exponents: $\frac{w^m}{w^n}=w^{m-n}$
$\frac{w^{-3}}{w^4}=w^{-3-4}$

Step2: Calculate exponent value

Compute the exponent: $-3-4=-7$, so we get $w^{-7}$

Step3: Convert to positive exponent

Use rule $w^{-k}=\frac{1}{w^k}$ to rewrite:
$w^{-7}=\frac{1}{w^7}$

Answer:

$\frac{1}{w^7}$