Let (17)^3.5 x (17)^x = 17⁸.

Then, (17)^{3.5 + x} = 17⁸.

So, 3.5 + x = 8

 x = (8 - 3.5)

 x = 4.5

Given:

(17)^3.5 x (17)^? = 17^8

To find: the value of the exponent '?'

Solution:

We can simplify the left-hand side of the equation using the laws of exponents:

(17)^3.5 x (17)^? = 17^8

(17)^(3.5 + ?) = 17^8

Since the bases are the same, we can equate the exponents:

3.5 + ? = 8

? = 8 - 3.5

? = 4.5

Therefore, the answer is option D (4.5).

Explanation:

• Exponents or powers are a way of representing repeated multiplication. For example, a^3 means "a multiplied by itself three times."
• The product of two exponential expressions with the same base can be simplified by adding their exponents. For example, a^3 x a^4 = a^(3+4) = a^7.
• In this problem, we are given the product of two exponential expressions with the same base, (17)^3.5 and (17)^?. We can simplify this product by adding the exponents: (17)^(3.5 + ?).
• We are also given that this product is equal to (17)^8, which allows us to equate the exponents and solve for the unknown exponent '?'.
• The final result is that '?' is equal to 4.5, which means that (17)^4.5 is the second term in the original product.

Formula:

• a^m x a^n = a^(m+n)

Key takeaways:

• When working with exponents, it is important to keep track of the base and the exponent separately, and to apply the laws of exponents to simplify expressions.
• Equating the exponents of exponential expressions with the same base can be a powerful technique for solving problems involving exponents.

If you think the solution is wrong then please provide your own solution below in the comments section .