Exercise 59
The expression \( (x + b)^{-2} \div (x + b)^{-5} \) equals:
-
\( (x + b)^{-3} \)
-
\( (x + b) \)
-
\( (x + b)^3 \)
-
\( (x + b)^{-7} \)
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\( (x + b)^7 \)
Try to solve it before checking the answer.
-
\( (x + b)^3 \)
\[
\begin{aligned}
(x + b)^{-2} \div (x + b)^{-5}
&= \frac{ (x + b)^{-2} }{ (x + b)^{-5} }
\\[2em]
&= (x + b)^{ -2 – (-5) }
\\[2em]
&= (x + b)^{-2 + 5} \\[2em] &= \boldsymbol{ (x + b)^3 }
\end{aligned}
\]