Show work. Simplify. Write answer in scientific notation:
(8.03 x 10^4) ^-4
Thank you!
(ab)^n = a^n b^n
So,
(8.03 x 10^4) ^-4
= 8.03^-4 x (10^4)^-4
= (2.405 x 10^-4) x 10^-16
= 2.405 x 10^-20
Could you please show me how you got the results of the 3rd & 4th line?
(2.405 x 10^4) x 10^-16
2.405 x 10^-20
When I solve I get these results:
3rd line) = 4157.7864 x 10^-16
4th line) = 4.1577864 x 10^-19
Thank you!
To simplify the expression (8.03 x 10^4) ^-4 and write the answer in scientific notation, we need to raise the number inside the parentheses to the power of -4.
First, let's simplify the expression inside the parentheses:
(8.03 x 10^4) ^-4
To raise a number to a negative exponent, we can take the reciprocal of the number raised to the positive exponent. So, we can rewrite the expression as:
(1 / (8.03 x 10^4)) ^4
Now, let's simplify further by evaluating the reciprocal:
1 / (8.03 x 10^4)
To divide by a number in scientific notation, we can divide the numbers in front and subtract the exponents. So, we have:
1 / 8.03 = 0.12427923844
The exponent remains the same, so we have:
0.12427923844 x 10^(-4)
Now, let's raise this value to the power of 4:
(0.12427923844 x 10^(-4)) ^4
To raise a number in scientific notation to a power, we raise the number before the "x" and multiple the exponent by the power. So, we have:
0.12427923844^4 x 10^(-4 x 4)
Calculating the value inside the parentheses, we get:
0.12427923844^4 = 0.0002885815
Now, let's calculate the exponent:
-4 x 4 = -16
Combining the results, we have:
0.0002885815 x 10^(-16)
Finally, to write this answer in scientific notation, we need to move the decimal point after the first nonzero digit. Therefore, the final answer is:
2.885815 x 10^(-13)