Simplify:
a) 8^2 = 64 ... correct?
b) 8^-2 = 1/8^2 ... correct?
c) (1/8)^2 = 1/64??
d) (1/8)^-2 = 1/64??
e) -8^2 = 64??
f) (-8)^2 64??
Please let me know if these are correct.
Thank you!
yes they are all correct, i tried them on my calculator.
Thank you!!
d) is not correct
(1/8)^-2
= (8/1)^+2
= 64
be careful with e) and f)
e) -8^2 = -64
it means -(8)(8)
f) (-8)^2 = +64
it means (-8)(-8)
i guess i made the same mistake she did?
Let's check if each of these statements is correct:
a) To simplify 8^2, you raise the base (8) to the exponent (2), which means multiplying 8 by itself. 8^2 = 8 * 8 = 64. So, yes, the statement is correct.
b) To simplify 8^-2, you need to take the reciprocal of 8^2. The reciprocal of any number is 1 divided by that number. So, 8^-2 = 1/8^2. And as we know, 8^2 is equal to 64. Therefore, 8^-2 = 1/64. So, yes, the statement is correct.
c) The statement (1/8)^2 = 1/64 is correct. To simplify (1/8)^2, you need to raise the numerator (1) to the exponent (2) and raise the denominator (8) to the exponent (2) as well. 1^2 = 1, and 8^2 = 64. So, (1/8)^2 = 1/64.
d) The statement (1/8)^-2 = 1/64 is also correct. To simplify (1/8)^-2, you need to take the reciprocal of (1/8)^2, just like in part b. So, (1/8)^-2 = 1/(1/8)^2 = 1/64.
e) The statement -8^2 = 64 is incorrect. According to the order of operations, you first need to raise 8 to the exponent of 2, which gives you 64. After that, you apply the negative sign. So, -8^2 = -64.
f) The statement (-8)^2 = 64 is correct. In this case, the parentheses change the order of operations. First, you square the number inside the parentheses, which is 8. Then you apply the negative sign outside the parentheses. So, (-8)^2 = 64.
Therefore, the correct statements are:
a) 8^2 = 64
b) 8^-2 = 1/64
c) (1/8)^2 = 1/64
d) (1/8)^-2 = 1/64
e) -8^2 = -64
f) (-8)^2 = 64