Question

(2xy^2 times 2y^4)^3 simplify using algebra 1 exponential rules

Answer 1

To simplify the expression \((2xy^2 \times 2y^4)^3\) using the exponential rules, we can follow these steps:

1. **Multiply the terms inside the parentheses**:
\[
2xy^2 \times 2y^4 = (2 \times 2) \times (x) \times (y^2 \times y^4) = 4x \times y^{2+4} = 4xy^6
\]

2. **Now, raise this result to the power of 3**:
\[
(4xy^6)^3
\]

3. **Apply the power of a product rule**:
\[
(a \times b)^n = a^n \times b^n
\]
This gives us:
\[
4^3 \times (x)^3 \times (y^6)^3
\]

4. **Calculate each part**:
- \(4^3 = 64\)
- \(x^3 = x^3\)
- \((y^6)^3 = y^{6 \times 3} = y^{18}\)

5. **Combine these results**:
\[
64x^3y^{18}
\]

Thus, the simplified expression is:
\[
\boxed{64x^3y^{18}}
\]