Positive Exponents 976Ab1

1. **State the problem:** Rewrite the expression $$\left(\frac{5x}{3yz}\right)^{-\frac{6}{5}}$$ using only positive rational exponents. 2. **Recall the rule:** A negative exponent means the reciprocal of the base raised to the positive exponent. That is, $$a^{-m} = \frac{1}{a^m}$$. 3. **Apply the negative exponent rule:** $$\left(\frac{5x}{3yz}\right)^{-\frac{6}{5}} = \frac{1}{\left(\frac{5x}{3yz}\right)^{\frac{6}{5}}}$$ 4. **Rewrite the denominator:** $$\left(\frac{5x}{3yz}\right)^{\frac{6}{5}} = \frac{(5x)^{\frac{6}{5}}}{(3yz)^{\frac{6}{5}}}$$ 5. **Combine the result:** $$\frac{1}{\frac{(5x)^{\frac{6}{5}}}{(3yz)^{\frac{6}{5}}}} = \frac{(3yz)^{\frac{6}{5}}}{(5x)^{\frac{6}{5}}}$$ 6. **Final expression with positive rational exponents:** $$\boxed{\frac{(3yz)^{\frac{6}{5}}}{(5x)^{\frac{6}{5}}}}$$ This expression uses only positive rational exponents as required.