Simplify the expression.$\left(-\frac{3}{4}p\right)^3$(−34​p)3​The simplified expression is .

1. Break Down the Problem

We need to simplify the expression $\left(-\frac{3}{4}p\right)^3$.

2. Relevant Concepts

To simplify the expression, we will use the property of exponents which states that $(ab)^n = a^n \cdot b^n$. We will apply this property to both the coefficient and the variable.

3. Analysis and Detail

The expression can be broken down as follows: $\left(-\frac{3}{4}p\right)^3 = \left(-\frac{3}{4}\right)^3 \cdot p^3$ Now we calculate $\left(-\frac{3}{4}\right)^3$: $\left(-\frac{3}{4}\right)^3 = -\left(\frac{3^3}{4^3}\right) = -\left(\frac{27}{64}\right) = -\frac{27}{64}$

Next, we calculate $p^3$: $p^3 = p^3$

Combining these results, we have: $\left(-\frac{3}{4}p\right)^3 = -\frac{27}{64}p^3$

4. Verify and Summarize

I verified the calculations for both parts:

• $\left(-\frac{3}{4}\right)^3 = -\frac{27}{64}$ is correct.
• $p^3$ remains unchanged.

Final Answer

The simplified expression is: $-\frac{27}{64}p^3$