1. Simplify with positive exponents (evaluate where possible AFTER simplifying) CHOOSE 2
a) 12^15 × 12^21/(12^3)^-2
To simplify the expression, we can start by evaluating the numerator and denominator separately.
a) The numerator, 12^15 × 12^21, can be simplified by adding the exponents together since the bases are the same:
12^15 × 12^21 = 12^(15+21) = 12^36
Now, let's simplify the denominator. The expression inside the parentheses, (12^3)^-2, can be simplified by raising 12^3 to the power -2. This is equivalent to taking the reciprocal of 12^3 and squaring it:
(12^3)^-2 = (1/(12^3))^2 = (1/12^3)^2 = (1/1728)^2
Finally, we can simplify the expression by dividing the numerator by the denominator:
12^36 / (1/1728)^2
To evaluate further, we can simplify the denominator by squaring the reciprocal:
12^36 / (1/1728)^2 = 12^36 / (1^2 / 1728^2) = 12^36 / (1 / 2985984)
Now, we can simplify the division by multiplying the numerator by the reciprocal of the denominator:
12^36 / (1 / 2985984) = 12^36 * 2985984 = 352161460620395808
Therefore, the simplified expression is 352161460620395808.