Questions: v^10/-32u^20

Solution Steps

To simplify the expression \(\left(\frac{v^{2}}{-2 u^{4}}\right)^{5}\) without parentheses, we need to apply the power to both the numerator and the denominator separately. This involves raising \(v^2\) to the power of 5 and \(-2u^4\) to the power of 5. The negative sign in the denominator will also be affected by the power.

To simplify the expression \(\left(\frac{v^{2}}{-2 u^{4}}\right)^{5}\), we first apply the power of 5 to both the numerator and the denominator separately. This gives us:

\[ \left(v^2\right)^5 = v^{10} \]

\[ \left(-2 u^4\right)^5 = (-2)^5 \cdot (u^4)^5 = -32 \cdot u^{20} \]

Now, we combine the results from Step 1 to form a single fraction:

\[ \frac{v^{10}}{-32 u^{20}} \]

The expression \(\frac{v^{10}}{-32 u^{20}}\) can be rewritten by factoring out the negative sign:

\[ -\frac{v^{10}}{32 u^{20}} \]

Final Answer