Alright, so I'm doing questions on exponent laws for my grade 11 math couse, and I came across one and I've no idea how to answer it. Could someone please explain step by step? According to textbook, answer should be 16:
(2^3) / [(2^0)-(2^-1)]
That "-1" is a negative exponent in the last bit, just so you know.
Some of the exponential laws state that:
a0=1
a1=a
a-b=1/ab
In your case, a=2 (the base).
So these laws should enable you to evaluate each term of the denominator.
The answer should indeed be 16.
I appreciate your having inserted sufficient parentheses to render the expression unambiguous.
I hope I'm not asking too much, but it would be ace if you would type out the problem and the path to solving it just so I can compare and see where I'm going wrong?
Here it is. Post if help is needed.
(2^3) / [(2^0)-(2^-1)]
=8/(2^0-2^-1)
=8/(1- 1/2¹)
=8/(1- 1/2)
=8/(1/2)
=16
Sure! Let's break down the steps to solve the exponent expression (2^3) / [(2^0)-(2^-1)]:
Step 1: Simplify the exponents inside parentheses
Since (2^3) means 2 raised to the power of 3, we have 2^3 = 2 * 2 * 2 = 8.
Step 2: Simplify the exponents inside the brackets
- In the denominator, (2^0) means 2 raised to the power of 0, which is equal to 1. Any number raised to the power of 0 is always 1.
- In the denominator, (2^-1) means 1 / (2^1), which is equal to 1/2. When an exponent is negative, it represents taking the reciprocal of the number raised to the positive exponent.
Step 3: Substitute the simplified values back into the expression
Now, we can substitute the simplified values back into the expression:
(2^3) / [(2^0) - (2^-1)]
Becomes:
8 / (1 - 1/2)
Step 4: Perform the subtraction inside the brackets
To subtract fractions with different denominators, we need to find a common denominator. Here, the common denominator is 2. So, we have:
8 / (1 - 1/2) = 8 / (2/2 - 1/2) = 8 / (1/2) = 8 * 2/1 = 16
Therefore, the final answer is 16.