Simplifying Algebraic Expressions with Exponents
Sure, to simplify the expression provided in the image, we need to follow the rules of algebra and exponents.
The expression in the image is:
(10 × 5^n^4 + 125 × 5^n^2) / (3 × 5^n^3 + 20 × 5^n^1)
Let's simplify the numerator and the denominator separately.
First, we can factor out the greatest common factor in the numerator, which is 5^n^2:
= 5^n^2 (10 × 5^n^2 + 125) / (3 × 5^n^3 + 20 × 5^n^1)
And then we can do the same for the denominator, where the greatest common factor is 5^n^1:
= 5^n^2 (10 × 5^n^2 + 125) / 5^n^1 (3 × 5^n^2 + 20)
Now, let's simplify the terms inside the parentheses:
Numerator: 10 × 5^n^2 + 125 can be simplified to 5^n^2 + 125. Since no further simplification can be done inside the parentheses (assuming the "+ 125" is not supposed to have a power of 5 associated with it), let's keep it as is.
Denominator: 3 × 5^n^2 + 20 simplifies to 3 × 5^n^2 + 20. Again, assuming "20" does not have a power of 5 associated with it, there's no further simplification inside the parentheses.
So now we have:
= 5^n^2 (5^n^2 + 125) / 5^n^1 (3 × 5^n^2 + 20)
Now, let's simplify across the numerator and denominator by canceling common factors where possible. We can cancel one 5^n^1 from both the numerator and the denominator:
= 5^n (5^n^2 + 125) / (3 × 5^n^2 + 20)
We cannot simplify further without knowing the value of n. If n is such that n^2, n^1, and the simple numerical terms 125 and 20 can be simplified further, we'd do that. Otherwise, this is the simplified form of the given expression. Please note that the superscripts in the original expression might be ambiguous due to the resolution and angle of the photo. If the powers are not correctly interpreted, please provide more information or adjust the expression accordingly.
