To solve \(\left(\frac{25}{16}\right)^{-\frac{3}{2}}\), follow these steps:

1. **Apply the negative exponent:**
   \[
   \left(\frac{25}{16}\right)^{-\frac{3}{2}} = \left(\frac{16}{25}\right)^{\frac{3}{2}}
   \]
   When you have a negative exponent, you can take the reciprocal of the base and make the exponent positive.

2. **Apply the fractional exponent:**
   \[
   \left(\frac{16}{25}\right)^{\frac{3}{2}} = \left(\left(\frac{16}{25}\right)^{\frac{1}{2}}\right)^3
   \]
   The \(\frac{1}{2}\) exponent is equivalent to taking the square root.

3. **Calculate the square root of the fraction:**
   \[
   \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}
   \]

4. **Raise the result to the power of 3:**
   \[
   \left(\frac{4}{5}\right)^3 = \frac{4^3}{5^3} = \frac{64}{125}
   \]

So, \(\left(\frac{25}{16}\right)^{-\frac{3}{2}} = \frac{64}{125}\).

Would you like further details or have any questions?

### Related Questions
1. How do you simplify expressions with negative exponents?
2. What is the meaning of a fractional exponent?
3. How do you find the cube of a fraction?
4. What is the general rule for exponents when dealing with a fraction?
5. How do you convert a fraction to a decimal and vice versa?
6. What is the value of \(\left(\frac{64}{125}\right)^{\frac{2}{3}}\)?
7. How do you simplify \(\left(\frac{9}{4}\right)^{-\frac{1}{2}}\)?
8. How would you solve \(\left(\frac{81}{16}\right)^{-\frac{3}{4}}\)?

### Tip:
When dealing with fractional exponents, remember that the numerator represents the power, and the denominator represents the root.

Discover how to solve the expression (25/16)^(-3/2) step-by-step with clear explanations. Learn about negative exponents, fractional exponents, and more. Suitable for high school students and anyone interested in exponent rules.

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