Simplify the expression. Write the result using positive exponents only.
-$\frac { 4 ^ { - 6 } x ^ { - 6 } y ^ { 4 } } { 4 ^ { - 3 } x ^ { - 9 } y ^ { 8 } }$
A) $\frac { x ^ { 3 } } { 64 y ^ { 4 } }$
B) $\frac { 3 x ^ { 3 } } { y ^ { 4 } }$
C) $\frac { 64 } { x ^ { 3 } y ^ { 4 } }$
D) $\frac { 1 } { 64 x ^ { 9 } y ^ { 4 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, apply the quotient rule for exponents: $a^m / a^n = a^{m-n}$. For the given expression, $4^{-6}/4^{-3} = 4^{-6-(-3)} = 4^{-3}$, $x^{-6}/x^{-9} = x^{-6-(-9)} = x^3$, and $y^4/y^8 = y^{4-8} = y^{-4}$. Simplifying gives $4^{-3}x^3y^{-4}$, which can be rewritten as $x^3 / (4^3y^4) = x^3 / (64y^4)$, matching choice A.

Simplify the Expression 4−6x−6y44−3x−9y8\frac { 4 ^ { - 6 } x ^ { - 6 } y ^ { 4 } } { 4 ^ { - 3 } x ^ { - 9 } y ^ { 8 } }4−3x−9y84−6x−6y4​

Simplify the Expression $\frac { 4 ^ { - 6 } x ^ { - 6 } y ^ { 4 } } { 4 ^ { - 3 } x ^ { - 9 } y ^ { 8 } }$