Simplify 26÷negitive*13

Solution:

Step 1: Simplify the expression by addressing the denominator.

• Step 1.1: Apply the exponential function to the denominator. $26 \div \text{negative} \left( e^{1} \right) \times 13$

• Step 1.2: Repeat the application of the exponential function. $26 \div \text{negative} \left( e^{1} \times e^{1} \right) \times 13$

• Step 1.3: Utilize the exponentiation rule $a^{m} \times a^{n} = a^{m + n}$. $26 \div \text{negative} e^{1 + 1} \times 13$

• Step 1.4: Perform the addition of the exponents. $26 \div \text{negative} e^{2} \times 13$

• Step 1.5: Combine the imaginary units by adding their exponents.

  • Step 1.5.1: Rearrange the imaginary units. $26 \div \text{neg} \left( i \times i \right) \text{ative} e^{2} \times 13$
  • Step 1.5.2: Multiply the imaginary units. $26 \div \text{neg} i^{2} \text{ative} e^{2} \times 13$

Step 2: Replace $i^{2}$ with $-1$. $26 \div \text{neg} \times -1 \text{ative} e^{2} \times 13$

Step 3: Express the division as a fraction. $\frac{26}{\text{neg} \times -1 \text{ative} e^{2}} \times 13$

Step 4: Position $-1$ before the 'neg' term. $\frac{26}{-1 \times (\text{neg}) \text{ative} e^{2}} \times 13$

Step 5: Place the negative sign in front of the fraction. $- \frac{26}{\text{neg} \text{ative} e^{2}} \times 13$

Step 6: Execute the multiplication of $- \frac{26}{\text{neg} \text{ative} e^{2}}$ and $13$.

• Step 6.1: Multiply $13$ by $-1$. $-13 \times \frac{26}{\text{neg} \text{ative} e^{2}}$
• Step 6.2: Combine $-13$ with the fraction. $\frac{-13 \times 26}{\text{neg} \text{ative} e^{2}}$
• Step 6.3: Multiply $-13$ and $26$. $\frac{-338}{\text{neg} \text{ative} e^{2}}$

Step 7: Bring the negative sign out in front of the fraction. $- \frac{338}{\text{neg} \text{ative} e^{2}}$

Knowledge Notes:

The problem-solving process involves simplifying an expression that contains a division by a negative exponentiated value. The steps include manipulating the expression using properties of exponents and imaginary numbers. Here are the relevant knowledge points:

1. Exponentiation: Raising a number to a power, such as $e^{1}$, where $e$ is the base of the natural logarithm.

2. Power Rule: A rule for simplifying expressions with exponents, stating that $a^{m} \times a^{n} = a^{m + n}$.

3. Imaginary Unit: The imaginary unit $i$ is defined as $\sqrt{-1}$, and $i^{2} = -1$.

4. Negative Numbers: A negative number times another negative number results in a positive number.

5. Fraction Representation: Division can be represented as a fraction, where the numerator is the dividend and the denominator is the divisor.

6. Combining Terms: Multiplication and division operations are performed to combine terms into a simpler form.

7. Negative Sign Placement: A negative sign can be moved in front of a fraction to indicate that the entire fraction is negative.

The solution involves using these principles to simplify the given expression step by step, ensuring that the negative signs and imaginary units are handled correctly to arrive at the final simplified result.