Simplify the expression. Write your answer as a power.$\left(\left(-\frac{3}{4}\right)^5\right)^2$((−34​)5)2​The simplified expression is .

To simplify the expression $\left(\left(-\frac{3}{4}\right)^5\right)^2$, you need to follow these steps:

1. First, you need to understand the rule of exponents which states that $(a^m)^n = a^{m*n}$.

2. Apply this rule to the given expression. This gives you $\left(-\frac{3}{4}\right)^{5*2}$.

3. Simplify the exponent 5*2 to get 10. So, the expression becomes $\left(-\frac{3}{4}\right)^{10}$.

4. Since any number raised to an even power is positive, the expression simplifies to $\left(\frac{3}{4}\right)^{10}$.

So, the simplified expression is $\left(\frac{3}{4}\right)^{10}$.

To simplify the expression $\left(\left(-\frac{3}{4}\right)^5\right)^2$, you need to follow these steps:

1. First, you need to understand the order of operations. In this case, you should simplify the expression inside the innermost parentheses first, which is $\left(-\frac{3}{4}\right)^5$.

2. To calculate $\left(-\frac{3}{4}\right)^5$, you need to multiply -3/4 by itself 5 times. Since the power is odd, the result will be negative. The absolute value of the result is $\left(\frac{3}{4}\right)^5 = \frac{243}{1024}$, so the result is $-\frac{243}{1024}$.

3. Next, you need to raise this result to the power of 2, which is the operation indicated by the outer parentheses. So, you calculate $\left(-\frac{243}{1024}\right)^2$.

4. Squaring a number means multiplying it by itself, and the square of any number, whether it's positive or negative, is always positive. So, $\left(-\frac{243}{1024}\right)^2 = \left(\frac{243}{1024}\right)^2 = \frac{59049}{1048576}$.

So, the simplified expression is $\frac{59049}{1048576}$.