Subjects algebra

Exponent Simplification 1B0A0A

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Simplify the expression $$\left(s^{-\frac{4}{3}}\right)^5$$ assuming all variables are positive. 2. **Recall the exponentiation rule:** When raising a power to another power, multiply the exponents: $$\left(a^m\right)^n = a^{m \times n}$$ 3. **Apply the rule:** $$\left(s^{-\frac{4}{3}}\right)^5 = s^{-\frac{4}{3} \times 5} = s^{-\frac{20}{3}}$$ 4. **Rewrite with positive exponents:** Since the exponent is negative, use the rule: $$a^{-m} = \frac{1}{a^m}$$ So, $$s^{-\frac{20}{3}} = \frac{1}{s^{\frac{20}{3}}}$$ 5. **Final answer:** $$\boxed{\frac{1}{s^{\frac{20}{3}}}}$$ This is the simplified form with all positive exponents.