(1/25) 3/2 is exponets simplify answer without exponents

To simplify the expression \( \left(\frac{1}{25}\right)^{\frac{3}{2}} \) without using exponents, follow these steps:

1. **Simplify the base**: \( \frac{1}{25} \) can be rewritten as \( \left(\frac{1}{5}\right)^2 \).

   \[
   \left(\frac{1}{25}\right)^{\frac{3}{2}} = \left(\left(\frac{1}{5}\right)^2\right)^{\frac{3}{2}}
   \]

2. **Apply the power of a power rule**: \( \left(a^m\right)^n = a^{m \times n} \).

   \[
   \left(\left(\frac{1}{5}\right)^2\right)^{\frac{3}{2}} = \left(\frac{1}{5}\right)^{2 \times \frac{3}{2}} = \left(\frac{1}{5}\right)^3
   \]

3. **Simplify the exponent**: \( \left(\frac{1}{5}\right)^3 \) means multiplying \( \frac{1}{5} \) by itself three times.

   \[
   \left(\frac{1}{5}\right)^3 = \frac{1}{5} \times \frac{1}{5} \times \frac{1}{5} = \frac{1}{125}
   \]

So, \( \left(\frac{1}{25}\right)^{\frac{3}{2}} \) simplifies to \( \frac{1}{125} \).

Would you like more details or have any questions? Here are 5 related questions:

1. How do you simplify expressions with fractional exponents involving larger bases?
2. How do you convert a fractional exponent into a radical expression?
3. How would you simplify \( \left(16\right)^{\frac{3}{4}} \) without using exponents?
4. What is the general rule for simplifying \( a^{\frac{m}{n}} \) expressions?
5. How do you deal with negative exponents in fractions?

**Tip:** Fractional exponents can be rewritten as radicals. For example, \( x^{\frac{1}{n}} \) is the same as the \( n \)-th root of \( x \).

Learn how to simplify the expression (1/25)^(3/2) without using exponents. Follow our detailed step-by-step guide, which covers fractional exponents and the power of a power rule. Suitable for high school students.

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