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Question

Simplify the expression. Write the answer using scientific notation.

24.8 x 1022

2.48 x 1012

24.8 x 1011

1.02 x 1012

Answer 1

To simplify the expression, it's important to understand the terms involved and the given expression in this case. However, it is not clear if these numbers are supposed to be multiplied, divided, added, or subtracted from the given question. Given the scientific notation context, I'll assume we're working with multiplication.

Given expression:

$$(24.8\times {10}^{22})\times (2.48\times {10}^{12})\times (24.8\times {10}^{11})\times (1.02\times {10}^{12})$$

We can simplify the multiplication of numbers and the addition of exponents step-by-step. Note that scientific notation requires the number to be in the format $a\times {10}^n$, where $a$ is a number between 1 and 10.

First, multiply the coefficients:
$$24.8\times 2.48\times 24.8\times 1.02$$

Second, sum the exponents of 10:
$$(22+12+11+12)$$

Now let's calculate each part:

### Coefficient Multiplication:
$$24.8\times 2.48\times 24.8\times 1.02$$

You can use a calculator or simplify step-by-step:

1. $24.8\times 2.48=61.504$
2. $61.504\times 24.8=1525.2992$
3. $1525.2992\times 1.02=1555.805904$

### Exponent Sum:
$$22+12+11+12=57$$

Now combine the results into a singly scientific notation:

$$1555.805904\times {10}^{57}$$

However, proper scientific notation requires the coefficient to be between 1 and 10. Adjust the coefficient:

$$1555.805904=1.555805904\times {10}^3$$

Then in scientific notation:

$$1.555805904\times {10}^3\times {10}^{57}=1.555805904\times {10}^{60}$$

So the simplified and properly formatted answer in scientific notation is:

$$1.555805904\times {10}^{60}$$

Note that scientific notation typically only takes the most significant digits (depending on the precision required). If you need a more concise result:

$$1.556\times {10}^{60}$$