Simplify the exponential expression: 28x⁴y² divided by 16x⁷y to the negative third.

Step-by-step solution

1. 1

   Split the work into three independent pieces. The coefficients, the powers of $x$ and the powers of $y$ can each be reduced on their own.

2. 2

   Reduce the coefficients. $\dfrac{28}{16} = \dfrac{7}{4}$ after dividing both by the common factor $4$.

3. 3

   Subtract the x exponents. $x^{4-7} = x^{-3}$. The larger power sits in the denominator, so the result is negative.

4. 4

   Subtract the y exponents. $y^{2-(-3)} = y^{5}$. Subtracting a negative exponent adds the two magnitudes — this is the step most often botched.

5. 5

   Rewrite with positive exponents only. $\dfrac{7}{4}x^{-3}y^{5} = \dfrac{7y^5}{4x^3}$.

6. 6

   Check numerically. At $x = 2$, $y = 2$: the original is $\dfrac{28 \cdot 16 \cdot 4}{16 \cdot 128 \cdot 0.125} = \dfrac{1792}{256} = 7$, and $\dfrac{7 \cdot 32}{4 \cdot 8} = 7$.