Simplify Exponents

Example on how to simplify exponents.

Example 1

For all nonzero $x$ and $y$, $(\tfrac{16 x^3 y^{-3}}{4^3 x^{-1} y^{-2}})^{-3}=$
  1. $\dfrac{64 y^{-3}}{x^{12}}$

  2. $\dfrac{64 y^{-3}}{x^{-12}}$

  3. $\dfrac{64 y^3}{x^{12}}$

  4. $\dfrac{64 y^{3}}{x^{-12}}$

  5. $64$

Solution

Simplify expressions with exponents.

  1. We start by simplifying inside the parentheses

    $\dfrac{16}{4^3}=\dfrac{4^2}{4^3}=\dfrac{1}{4}$

    $\dfrac{x^3}{x^{-1}}=x^4$

    $\dfrac{y^{-3}}{y^{-2}}=y^{-1}$

  2. 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