evaluate each of the following:
2⁷*3⁴
6²*3⁴/2²
To evaluate each of the following expressions, we need to apply the rules of exponents.
1) 2⁷ * 3⁴:
Using the rule of exponents that states aⁿ * aᵐ = a^(n + m), we can simplify this expression:
2⁷ * 3⁴ = 2^(7 + 4) * 3^(4) = 2^11 * 3^4 = 2048 * 81 = 166,464.
2) 6² * 3⁴/2²:
Again, applying the rule of exponents that states aⁿ / aᵐ = a^(n - m), we can simplify this expression:
6² * 3⁴/2² = 6^(2 + 4) * 3⁴ / 2² = 6^6 * 3^4 / 2².
Now, using the rule of exponents that states (a/b)ⁿ = aⁿ / bⁿ, we can further simplify the expression:
6^6 * 3^4 / 2² = (6^6 * 3^4) / 2² = (6^6 / 2²) * 3^4 = 7776 * 81 / 4 = 594,432 / 4 = 148,608.
Therefore, the evaluation of the expressions 2⁷ * 3⁴ and 6² * 3⁴/2² are 166,464 and 148,608, respectively.