Question

Which of these equations is correct? (1 point) (2 ^ 2) ^ 4 = 2 ^ 6; (8 ^ 3) ^ 2 = 8 ^ 9; (3 ^ 5) ^ - 2 = 1/(3 ^ - 19); (5 ^ - 3) ^ 6 = 1/(5 ^ 18)

Answer 1

Let's evaluate each of the equations one by one to determine which one is correct.

1. \((2^2)^4 = 2^6\):
- The left side: \((2^2)^4 = 2^{2 \cdot 4} = 2^8\)
- The right side: \(2^6\)
- So, \(2^8 \neq 2^6\). This equation is **false**.

2. \((8^3)^2 = 8^9\):
- The left side: \((8^3)^2 = 8^{3 \cdot 2} = 8^6\)
- The right side: \(8^9\)
- So, \(8^6 \neq 8^9\). This equation is **false**.

3. \((3^5)^{-2} = \frac{1}{(3^{-19})}\):
- The left side: \((3^5)^{-2} = 3^{-10}\)
- The right side: \(\frac{1}{(3^{-19})} = 3^{19}\)
- So, \(3^{-10} \neq 3^{19}\). This equation is **false**.

4. \((5^{-3})^6 = \frac{1}{(5^{18})}\):
- The left side: \((5^{-3})^6 = 5^{-18}\)
- The right side: \(\frac{1}{(5^{18})} = 5^{-18}\)
- So, \(5^{-18} = 5^{-18}\). This equation is **true**.

The correct equation is the fourth one: \((5^{-3})^6 = \frac{1}{(5^{18})}\).