Question
(17)3.5 x (17)? = 178
Answer: Option D
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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 .
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