x^(d) = 1600, where d = 8 (multiplication of exponents with the same base).
We are given the equation:
8^4 * 5^4 = x^d
Base and Exponent:
8^4: This means 8 is multiplied by itself 4 times.
5^4: This means 5 is multiplied by itself 4 times.
Multiplication of Exponents:
When two exponents have the same base, we add their powers to get the power of the resulting product.
Therefore, 8^4 * 5^4 = (8 * 5)^(4+4) = 40^8.
Unknown Variable and Power:
The equation states that this product is equal to x raised to some power d.
Solving for x and d:
Since 40^8 = x^d, we know that the base of both expressions is 40 and their powers are equal.
Therefore, d = 8 (the sum of the exponents in the product).
In conclusion, x^(d) = 1600, where d = 8.