Answer:
2^27
Step-by-step explanation:
Given the following expression:
[(2^10)^3 x (2^-10)] ÷ 2^-7
This can be easily simplified. Let us simplify the numerator first. To do that, we have
(2^10)^3 making use of the power rule of indices that says:
(A^a)^b = A^ab where a and b are powers, we have:
2^(10x3) = 2^30
Therefore the numerator becomes:
2^30 x 2^-10. Also making use of the multiplication rule that says:
A^a x A^b = A^(a + b), we have
2^30 x 2^-10 = 2^(30 – 10) = 2^20.
Now we have:
(2^20) ÷ (2^-7)
To simplify this, we need the division rule of indices which says:
A^a ÷ A^b = A^(a – b)
Therefore we have:
(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27
