Simplify and write in scientific notation.
(9 X 10^-3)^2
A. 8.1 X 10^-5
B. 81 X 10^-4
C. 81 X 10^-3
D. 8.1 X 10^-6
?
Evaluate 1/2a^-4 b^2 for a = -2 and b = 4.
A. 2
B. 1/2
C. 3
D. 4
B
81 * 10*-6
= 8.1 * 10^-5
I have no idea. use parentheses or write it like this
1
-----------
2 a^-4b^2
or do you mean this?
(1/2) a^-4 b^2
or maybe
1
------------- b^2
2 a^-4
This one: (1/2) a^-4 b^2
that is
b^2
------------
2 a^4
4^2
--------
2 (-2)^4
16
-------
2(16)
1/2
(9x10⁻⁴)(8x10⁷)
To simplify and write (9 x 10^-3)^2 in scientific notation, we need to multiply 9 x 10^-3 by itself:
(9 x 10^-3)^2 = (9 x 10^-3) x (9 x 10^-3)
When multiplying powers with the same base, we add the exponents:
= 9 x 9 x 10^-3 x 10^-3
= 81 x 10^-6
Therefore, the answer is 81 x 10^-6.
Now, let's evaluate 1/2a^-4 b^2 for a = -2 and b = 4:
We substitute the values of a and b into the expression:
1/2(-2)^-4 (4)^2
(-2)^-4 means taking the reciprocal and squaring. So, (-2)^-4 = 1/(-2)^4 = 1/16.
Now we have:
1/2(1/16)(4)^2
Since 1/2 x 1/16 is equal to 1/32, we can simplify further:
1/32(4)^2
(4)^2 means squaring 4, which results in 16. So, we have:
1/32 x 16
To simplify further, we divide 16 by 32:
1/2
Therefore, the answer is 1/2.