−15+4/5(15e−10)−10e
2e+23
2e-23
-2e-23
-2e+23
The answer is -2e+23
To simplify the expression −15+4/5(15e−10)−10e, let's break it down step by step:
1. Start by simplifying the exponent of e:
e^(-10) = 1/(e^10)
2. Substitute the simplified exponent back into the expression:
−15+4/5(15/e^10)−10e
3. Next, apply the distributive property by multiplying 4/5 with each term inside the parentheses:
−15 + (4/5 * 15) / e^10 − 10e
4. Simplify the multiplication:
−15 + 3/e^10 − 10e
5. Combine like terms:
−15 − 10e + 3/e^10
The simplified expression is: -15 - 10e + 3/e^10.
None of the options provided matches the simplified expression.
To solve the expression −15+4/5(15e−10)−10e, we need to apply the order of operations (PEMDAS/BODMAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Let's break down the expression step by step:
1. Start with the expression: −15+4/5(15e−10)−10e
2. Simplify the exponential term (15e−10):
Calculate 15 multiplied by e raised to the power of -10. The value of e is approximately 2.71828.
So, 15e−10 = 15 * 2.71828^(-10)
3. Simplify the multiplication term (4/5 * 15 * 2.71828^(-10)):
Calculate 4 divided by 5, then multiply the result by 15 and 2.71828^(-10).
The value of 2.71828^(-10) is approximately 0.00004987.
4. Substitute the exponential and multiplication values back into the expression:
−15 + (4/5 * 15 * 0.00004987) − 10e
5. Continue with the multiplication: (4/5 * 15 * 0.00004987):
Calculate (4/5) * 15 * 0.00004987.
6. Simplify the expression further by evaluating the multiplication: (⅘ * 15 * 0.00004987)
Calculate 4 divided by 5, then multiply the result by 15 and 0.00004987.
7. Substitute the multiplication value back into the expression:
−15 + (0.00009974) − 10e
8. Apply multiplication: −10e
Multiply -10 with the value of e.
9. Substitute the multiplication value back into the expression:
−15 + (0.00009974) − (10 * the value of e)
10. Simplify the expression further:
Evaluate -10 times the value of e.
By substituting the approximate value of e (approximately 2.71828), we can calculate the final answer:
−15 + (0.00009974) − (10 * 2.71828)
Simplifying further,
−15 + 0.00009974 − 27.1828
The final result is -27.18270026.
Therefore, none of the given options (-2e+23, -2e-23, 2e+23, 2e-23) matches the value of the expression −15+4/5(15e−10)−10e.