Calculate the Product: Solving 8^5 × 9^5

Choose the expression that corresponds to the following:

$8^5\times9^5=$

The problem given is to simplify the expression $8^5 \times 9^5$. This problem can be solved by applying the power of a product rule exponent rule.

Step-by-step solution:

• According to the power of a product rule, when two expressions with the same exponent are multiplied, the product can be written as a single power expression:
  $a^n \times b^n = (a \times b)^n$

• Using this rule, we can rewrite the given expression $8^5 \times 9^5$ as a single power:
  $(8 \times 9)^5$

• Therefore, the expression simplifies to:
  $(72)^5$

• We have represented $8^5 \times 9^5$ as $(72)^5$, which is its corresponding expression according to the power of a product rule.

By recognizing that $8^5 \times 9^5$ can be expressed as a single power of $72$, we confirm that the problem demonstrates the application of the power of a product rule. All of the expressions are mathematically the same and therefore the correct answer is (d) "All answers are correct".