SELECT All terms that are equivalent to 4 ^ 3 / 4 ^ 5
To simplify the expression 4^3 / 4^5, we can use the rule of exponents which states that for any nonzero number 'a' and integers 'm' and 'n', a^m / a^n = a^(m-n).
Applying this rule to 4^3 / 4^5, we have 4^(3-5) = 4^(-2).
So, the equivalent terms are:
1) 4 ^ 3 / 4 ^ 5
2) 4 ^ (-2)
To solve this problem, we can simplify the expression step-by-step.
Step 1: Simplify the numerator and denominator separately.
4^3 = 4 * 4 * 4 = 64
4^5 = 4 * 4 * 4 * 4 * 4 = 1024
Step 2: Divide 64 by 1024.
64 / 1024 = 0.0625
Therefore, the expression 4^3 / 4^5 is equivalent to 0.0625.
Additional equivalent terms would be:
- 1/16
- 1:16
- 6.25%
To solve this expression, we can use the properties of exponents.
First, let's simplify the expression:
4^3 means "4 raised to the power of 3", which can be calculated as 4 * 4 * 4, resulting in 64.
Similarly, 4^5 means "4 raised to the power of 5", which can be calculated as 4 * 4 * 4 * 4 * 4, resulting in 1024.
Now we have the expression 64 / 1024.
To find other terms that are equivalent to this expression, we need to simplify the division.
One way to simplify the division is by canceling out common factors between the numerator and denominator.
In this case, we can simplify 64/1024 by dividing both numbers by their greatest common divisor (GCD), which is 32.
64 ÷ 32 = 2, and 1024 ÷ 32 = 32.
So, the expression 64/1024 is equivalent to 2/32.
To find other terms that are equivalent to 2/32, we can simplify the fraction further by dividing both the numerator and denominator by their greatest common divisor, which is 2.
2 ÷ 2 = 1, and 32 ÷ 2 = 16.
So, the expression 2/32 is equivalent to 1/16.
Therefore, all terms that are equivalent to 4^3/4^5 are 2/32 and 1/16.