5^-4 - 5^-6/5^-3 +5^-5
i got 24/26, simplified would be 12/13. Am i correct?
To simplify the expression, let's understand the rules of exponents in order to compute the given expression step by step.
The rules of exponents state:
1. When you have a negative exponent, it can be moved to the denominator by flipping the base to the opposite exponent.
2. When you divide two numbers with the same base but different exponents, you subtract the exponents.
3. When you multiply two numbers with the same base, you add the exponents.
Now, let's simplify the expression step by step:
1. 5^-4 - 5^-6/5^-3 + 5^-5
Applying the rules of exponents:
2. (1/5^4) - (1/5^6)/(1/5^3) + 1/5^5
Simplifying further:
3. 1/625 - 1/(5^6) / (1/125) + 1/(5^5)
Simplifying the division by multiplying by the reciprocal:
4. 1/625 - 1 * (125/5^6) + 1/(5^5)
Applying the rule of exponents:
5. 1/625 - 125/5^6 + 1/(5^5)
Simplifying further by evaluating 5^6 and 5^5:
6. 1/625 - 125/15625 + 1/3125
Finding a common denominator to combine the fractions:
7. 1/625 - 125/15625 + 1/3125
Since all denominators are already the same, we can now combine the fractions:
8. [(1 * 15625) - (125 * 625) + (1 * 625)] / 625 * 3125
Computing the numerator:
9. [15625 - 78125 + 625] / 625 * 3125
Further simplifying the numerator:
10. [-61875 + 625] / 625 * 3125
Calculating the numerator:
11. [-61250] / 625 * 3125
Simplifying the denominator:
12. -61250 / 625 * 3125
Now, let's compute the final result:
13. -0.076 / 625 * 3125
Evaluating the expression:
14. -0.076 * (3125/625)
Performing the multiplication:
15. -0.076 * 5
Calculating the final answer:
16. -0.38
Therefore, the simplification of the expression 5^-4 - 5^-6/5^-3 + 5^-5 is approximately equal to -0.38.
Based on this calculation, it seems that your simplified answer of 12/13 is not correct.