Question

simplify
\[\left( 3x ^{7}y ^{7} \right)^{2}\div x ^{9}\]

Answer 1

Let's recall our exponent rules.
Rule 1) Exponents of the same base are added when bases are multiplied. \[x^5 * x^5 = x^{10}\]Rule 2) Exponents of the same base are subtracted when bases are divided.
Rule 3) Exponents that are raised to exponents are multiplied together.

Applying these rules, we get \[{3x^{7*2}y^{7*2} \over x^9} = {3x^{14}y^{14} \over x^9} = {3x^{14-9}y^{14}} = 3x^5y^{14}\]