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Example 1
For all nonzero $x$ and $y$, $(\tfrac{16 x^3 y^{-3}}{4^3 x^{-1} y^{-2}})^{-3}=$
- $\dfrac{64 y^{-3}}{x^{12}}$
- $\dfrac{64 y^{-3}}{x^{-12}}$
- $\dfrac{64 y^3}{x^{12}}$
- $\dfrac{64 y^{3}}{x^{-12}}$
- $64$
Solution
Simplify expressions with exponents.
- We start by simplifying inside the parentheses
$\dfrac{16}{4^3}=\dfrac{4^2}{4^3}=\dfrac{1}{4}$
$\dfrac{x^3}{x^{-1}}=x^4$
$\dfrac{y^{-3}}{y^{-2}}=y^{-1}$
- We now substitute into the main expression
$(\tfrac{16 x^3 y^{-3}}{4^3 x^{-1} y^{-2}})^{-3}=(\dfrac{1}{4} x^4 y^{-1})^{-3}=4^3 x^{-12}y^3=\dfrac{64 y^3}{x^{12}}$
Answer C
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