which expression is equivalent to 2^-3/2^-2 x 2^6
A 16
B 1/32
C 32
D 1/64
We can simplify the given expression using the rules of exponents. First, we distribute the negative exponent in the numerator:
2^(-3) = 1/2^3 = 1/8
Next, we distribute the negative exponent in the denominator:
2^(-2) = 1/2^2 = 1/4
Now we simplify the expression by combining the like terms:
(1/8)/(1/4) * 2^6
To divide fractions, we multiply by the reciprocal of the divisor:
(1/8) * (4/1) * 2^6 = (1 * 4)/(8 * 1) * 2^6
Simplifying the fraction gives:
4/8 * 2^6 = 1/2 * 2^6
Combining the fractions and simplifying the expression further:
= 1/2 * 64
= 64/2
= 32
Therefore, the expression 2^(-3)/2^(-2) * 2^6 is equivalent to 32.
The correct answer is C) 32