I need to simplify this.
(2^-1 . 7^-4)^-2
I thought that 2 was suppose to be multiplied with the -1, but that doesn't seem to make sense so I am confused. I know that PEDMAS needs to be used, just don't know how to apply it. Any help is appreciated!
(2^-1 . 7^-4)^-2
= (2^2)(7^8)
= 23059204
Those aren't any of my choices Here is what i got
2^2 . 7^8
2^5 . 7^5
1/2^5 . 7^5
1/2^2 . 7 ^8
sorry I went to the effort of calculating
2^2 . 7^8 for you.
Thanks! That is what I thought, but why is this the answer? How does the probelm work it self out to be like that?
multiply each of the inside terms by the outside term.
2^-1*1^-2 = combine exponents = 2^2
7^-4*1^-2 = combine exponents = 7^8
To simplify the expression (2^-1 . 7^-4)^-2, we need to apply the rules of exponents.
Let's break this down step by step:
Step 1: Simplify the inner expressions first. We have (2^-1 . 7^-4).
To simplify this, we can rewrite the negative exponents as reciprocals:
(2^-1 . 7^-4) = (1/2^1 . 1/7^4)
Simplifying further:
(1/2 . 1/7^4) = 1/(2 . 7^4)
Step 2: Now, let's evaluate the expression 1/(2 . 7^4).
Calculating the numerical value, we have:
1/(2 . 7^4) = 1/(2 . 2401) = 1/4802
Step 3: Finally, raise the result from Step 2 to the power of -2.
To do this, we can rewrite 1/4802 as 4802^-1 and then apply the exponent:
(4802^-1)^-2 = 4802^(-1 * -2) = 4802^2
Therefore, the simplified form of the expression (2^-1 . 7^-4)^-2 is 4802^2.