Question

Write with positive exponents. Simplify if po (-27)-²/³

Answer 1

To write with positive exponents, we follow the rule that an exponent of -a is equivalent to 1 over the base raised to the positive exponent a. In this case, (-27)-²/³ simplifies to 1/9.

Step-by-step explanation:

To write with positive exponents, we follow the rule that an exponent of -a is equivalent to 1 over the base raised to the positive exponent a. In this case, we have (-27)-²/³. Let's simplify it step-by-step:

1. First, we can rewrite (-27)-²/³ as 1/(-27)²/³.
2. Next, we can cube the base and square the exponent to simplify further. (-27)²/³ = 27²/³.
3. Now, we can calculate 27²/³. The cube root of 27 is 3, so 27²/³ = 3² = 9.
4. Finally, we divide 1 by 9 to get the final answer. 1/9.

Therefore, (-27)-²/³ simplifies to 1/9.