Question

factor using the given common factor. assume all variables represent positive real numbers.
7t^{-3}+t^{-4}; t^{-4}
7t^{-3}+t^{-4}=square (type your answer in factored form.)

Explanation:

Step1: Recall exponent rule

When dividing terms with the same base $a^m\div a^n=a^{m - n}$.

Step2: Divide each term by $t^{-4}$

For the first - term $7t^{-3}\div t^{-4}=7t^{-3-(-4)} = 7t$. For the second - term $t^{-4}\div t^{-4}=1$.

Step3: Factor out the common factor

$7t^{-3}+t^{-4}=t^{-4}(7t + 1)$.

Answer:

$t^{-4}(7t + 1)$