How do you evaluate 16(2^-3 - 4^-2)?
16 (1/8 - 1/16) = 16 (1/16) = 1
Remember
x^-n = 1 / x^n
To evaluate the expression 16(2^-3 - 4^-2), we can follow the order of operations (also known as PEMDAS/BODMAS).
Step 1: Simplify any exponents first.
2^-3 means 2 to the power of -3, and 4^-2 means 4 to the power of -2.
To simplify these expressions, we use the property that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
So, 2^-3 = 1 / 2^3 = 1/8, and 4^-2 = 1 / 4^2 = 1/16.
Now our expression becomes: 16 (1/8 - 1/16).
Step 2: Perform the subtraction inside the parentheses.
To subtract fractions, we need a common denominator.
The least common multiple (LCM) of 8 and 16 is 16, so we multiply the numerator and denominator of 1/8 by 2 to get a common denominator of 16.
The expression now becomes: 16 (2/16 - 1/16).
Step 3: Subtract the fractions.
When the denominators are the same, we can subtract the numerators directly.
2/16 - 1/16 = 1/16.
So, our expression becomes: 16 (1/16).
Step 4: Multiply 16 by 1/16.
Multiplying a number by 1/16 is the same as dividing it by 16, so the answer is:
16 * (1/16) = 1.
Therefore, the value of the expression 16(2^-3 - 4^-2) is 1.