List two different ways to write 3^7 as the product of two powers
explain why both of your expressions are equal to 3^7
1) One way to write 3^7 as the product of two powers is 3^5 * 3^2. This is equal to (3 * 3 * 3 * 3 * 3) * (3 * 3), which simplifies to 3^7.
2) Another way is 3^4 * 3^3. This is equal to (3 * 3 * 3 * 3) * (3 * 3 * 3), which also simplifies to 3^7.
Both expressions are equal to 3^7 because they follow the rule of exponentiation, which states that when multiplying two powers with the same base, you add their exponents. In both cases, the exponents of 3 are added correctly, resulting in the expression 3^7.