 # You've Unlocked a New GMAT® Question!

Nov 19, 2023

### Question

easy

$\frac{1}{{x}^{3}}+\frac{1}{{y}^{7}}=?$

$\frac{1}{{x}^{3}{y}^{7}}$

$\frac{2}{{x}^{3}{y}^{7}}$

$\frac{{x}^{3}+{y}^{3}}{{x}^{3}{y}^{7}}$

$\frac{{x}^{7}+{y}^{7}}{{x}^{3}{y}^{7}}$

$\frac{{x}^{3}+{y}^{7}}{{x}^{3}{y}^{7}}$

PRESENTED BY : Scott Woodbury-Stewart Founder and Expert GMAT Instructor Solution:

Since x3 is the highest (really, only) power of the base x, and since y7 is the highest (only) power of the base y, the LCD of these two fractions is (x3)(y7). Let’s convert each fraction to a denominator of (x3)(y7) and combine the fractions:

$\begin{array}{l}⇒\frac{{y}^{7}}{{y}^{7}}\left(\frac{1}{{x}^{3}}\right)+\frac{{x}^{3}}{{x}^{3}}\left(\frac{1}{{y}^{7}}\right)\\ ⇒\frac{{y}^{7}}{{x}^{3}{y}^{7}}+\frac{{x}^{3}}{{x}^{3}{y}^{7}}=\frac{{x}^{3}+{y}^{7}}{{x}^{3}{y}^{7}}\end{array}$

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