10^4+10^6 keep in exponent form

Answer 1

To keep the expression \(10^4 + 10^6\) in exponent form, you can factor out the smaller exponent, which is \(10^4\):

\[ 10^4 + 10^6 = 10^4(1 + 10^{6-4}) = 10^4(1 + 10^2) \]

So, the expression in exponent form is:

\[ 10^4(1 + 10^2) \]

You can also simplify \(1 + 10^2\):

\[ = 10^4(1 + 100) = 10^4 \cdot 101 \]

Thus, the final expression can be presented as:

\[ 10^4 \cdot 101 \]

However, if you're strictly looking to maintain the exponent form without evaluating \(1 + 10^2\) as a numeric factor, then the first factored form \(10^4(1 + 10^2)\) is the best representation in exponent form.

Answer 2

how did you get your answer

Answer 3

To simplify the expression \(10^4 + 10^6\) and keep it in exponent form, I used the following steps:

1. Identify the Terms: The expression consists of two terms, \(10^4\) and \(10^6\).

2. Factor Out the Smaller Exponent: It's often useful to factor out the common base raised to the smaller exponent. Here, \(10^4\) is smaller than \(10^6\). So, I factor out \(10^4\):

   \[ 10^4 + 10^6 = 10^4(1 + \frac{10^6}{10^4}) \]

3. Simplify the Fraction: When you divide \(10^6\) by \(10^4\), you can subtract the exponents:

   \[ \frac{10^6}{10^4} = 10^{6-4} = 10^2 \]

   Substituting this back into the expression gives:

   \[ 10^4(1 + 10^2) \]

4. Simplify Further: At this point, you can either leave it as \(10^4(1 + 10^2)\) or, if desired, evaluate \(1 + 10^2\):

   \[ 1 + 10^2 = 1 + 100 = 101 \]

   Thus, you can express it as:

   \[ 10^4 \cdot 101 \]

5. Final Expression: The result keeps the base \(10\) factored out, and in this form, it clearly shows the exponent related to the term \(10^4\), while \(101\) is a separate coefficient.

In summary, the main goal was to factor the expression in a way that keeps the powers of 10 together, which allows for a clearer representation of the equation in exponent form. Thus the final answer could be expressed as either:

\[ 10^4(1 + 10^2) \quad \text{or} \quad 10^4 \cdot 101 \]

depending on your requirements.