Question

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

Answer 1

To simplify the expression \((\frac{y^3 \cdot 2yx^2}{2xy^3})^4\), we'll follow these steps:

1. **Simplify the fraction inside the parentheses**:
\[
\frac{y^3 \cdot 2yx^2}{2xy^3} = \frac{2y^{3+1}x^2}{2xy^3}
\]
The \(2\) in the numerator and the \(2\) in the denominator cancel out:
\[
= \frac{y^4x^2}{xy^3}
\]
Now, we can separate the \(y\) terms and the \(x\) terms:
\[
= \frac{y^4}{y^3} \cdot \frac{x^2}{x}
\]
Using the rule \(a^m / a^n = a^{m-n}\):
\[
= y^{4-3} \cdot x^{2-1} = y^1 \cdot x^1 = yx
\]

2. **Raise the simplified expression to the power of 4**:
\[
(yx)^4
\]
Using the power of a product rule \((ab)^n = a^n b^n\):
\[
= y^4 x^4
\]

Thus, the simplified expression is:
\[
\boxed{y^4 x^4}
\]