Simplify the expression. $$ \frac{\left(-9 y^{4}\right)^{2}\left(y^{4}\right)^{5}}{9 y}=\square $$

Question

UpStudy AI · Accepted Answer

To simplify the expression:

$$
\frac{\left(-9 y^{4}\right)^{2}\left(y^{4}\right)^{5}}{9 y}
$$

**Step 1: Simplify each part of the numerator**

1. $$\left(-9 y^{4}\right)^{2}$$:
   $$
   (-9)^2 \cdot (y^4)^2 = 81 \cdot y^{8} = 81 y^{8}
   $$

2. $$\left(y^{4}\right)^{5}$$:
   $$
   y^{4 \times 5} = y^{20}
   $$

**Step 2: Multiply the simplified parts of the numerator**

$$
81 y^{8} \cdot y^{20} = 81 y^{28}
$$

**Step 3: Divide by the denominator**

$$
\frac{81 y^{28}}{9 y}
$$

**Step 4: Simplify the division**

1. Divide the coefficients:
   $$
   \frac{81}{9} = 9
   $$

2. Subtract the exponents for the $$y$$ terms:
   $$
   y^{28} \div y^{1} = y^{27}
   $$

**Final Simplified Expression:**

$$
9y^{27}
$$

**Answer:** 
$$ 9\, y^{27} $$
The simplified expression is $$9y^{27}$$.

Simplify the expression. \[ \frac{\left(-9 y^{4}\right)^{2}\left(y^{4}\right)^{5}}{9 y}=\square \]