Question

Finally, consider the expression (6.67×10^−11)(5.97×10^24)/(6.38×10^6)^2. Determine the values of a and k when the value of this expression is written in scientific notation. Enter a and k, separated by commas.

Answer 1

To express the given expression in scientific notation, we find a = 9.78 and k = -1 after evaluating the expression using the laws of exponentiation and division.

Step-by-step explanation:

The student's question involves evaluating an expression using scientific notation and expressing the result in proper scientific notation.

To solve (6.67×10−11)(5.97×1024) / (6.38×106)2, we need to use the laws of exponentiation and multiplication. Simplify the expression within the numerator and denominator separately before dividing them.

Numerator: (6.67×10−11)(5.97×1024) = 39.8309×1013

Denominator: (6.38×106)2 = 40.7044×1012

Divide the simplified numerator by the simplified denominator:
39.8309×1013 / 40.7044×1012 = 0.978×101

To express this in proper scientific notation, rewrite 0.978×101 as 9.78×10−0.

Therefore, the values of a and k when the value of this expression is written in scientific notation are a = 9.78 and k = −0.

Answer 2

`x=9.78* 10^0`

Step-by-step explanation:

In this case, we need to find the value of expression :

`x=((6.67* 10^(-11))* (5.97* 10^(24)))/((6.38* 10^6)^2)`

On solving, we get the value of given expression as :

x = 9.7827

In scientific notation, we get the value of x as :

`x=a* 10^k`

`x=9.78* 10^0`

a = 9.78

k = 0

Hence, this is the required solution.