Question

Simplify (8 x 10⁻¹³) - (3.7 x 10⁻¹⁵).

1) 4.3 x 10⁻¹⁵
2) 4.3 x 10⁻¹³
3) 7.963 x 10⁻¹⁵
4) 7.963 x 10⁻¹³

Answer 1

Answer: number 2) 4.3 x 10⁻¹³

Answer 2

To simplify the given expression, convert both terms to have the same exponent for the powers of ten. The simplified expression becomes 7.963 x 10⁻¹³, which is option 4).

Step-by-step explanation:

The question asks you to simplify the expression (8 x 10⁻¹³) - (3.7 x 10⁻¹⁵). To do this, both terms must have the same exponent so that they can be combined. To put them on equal footing, notice that 10⁻¹³ is the same as 10⁻¹⁵ multiplied by 10² because if you add the exponents -13 + 2, you get -11.

Now let's convert 8 x 10⁻¹³ into terms of 10⁻¹⁵:
8 x 10⁻¹³ = 8 x (10² x 10⁻¹⁵) = 8 x 10² x 10⁻¹⁵ = 800 x 10⁻¹⁵.

So now our expression becomes:
(800 x 10⁻¹⁵) - (3.7 x 10⁻¹⁵) = (800 - 3.7) x 10⁻¹⁵

We subtract 3.7 from 800, which gives us 796.3, and thus:
796.3 x 10⁻¹⁵.

To write this in scientific notation, we move the decimal point so that there's only one non-zero digit to the left, which gives us:
7.963 x 10⁻¹³.

Therefore, the simplified expression is 7.963 x 10⁻¹³, which corresponds to option 4).