Using the quotient rule of exponents, what is an equivalent form of two with a small eight on top of it divided by two with a small four on top of it is the answer to when they small 32 on top of it or two with the small tube on top of it or two with a small 12 on top of it or two with a small core on top of it

Question

Using the quotient rule of exponents, what is an equivalent form of two with a small eight on top of it divided by two with a small four on top of it is the answer to when they small 32 on top of it or two with the small tube on top of it or two with a small 12 on top of it or two with a small core on top of it

Answer 1

To simplify the expression, let's write out the given expression in a clear manner first:

$2^{8} \div 2^{4} = 2^{32} \div 2^{2} \div 2^{12} \div 2$

Now, let's apply the quotient rule of exponents. According to the quotient rule, when dividing two numbers with the same base, we subtract the exponents:

$2^{8-4} = 2^{32-2-12-1}$

This simplifies to:

$2^{4} = 2^{17}$

Therefore, an equivalent form of the given expression is $2^{4} = 2^{17}$.

Answer 2

To simplify the expression using the quotient rule of exponents, we can subtract the exponents:

\[ \frac{2^8}{2^4} = 2^{8-4} = 2^4 \]

Now, we can apply the quotient rule once again:

\[ \frac{2^4}{2^{32}} = 2^{4-32} = 2^{-28} \]

Next, we can simplify the expression with the exponent of 2:

\[ 2^{-28} = \frac{1}{2^{28}} \]

Finally, we can write the equivalent form as:

\[ \frac{1}{2^{28}} \]

Answer 3

To find an equivalent form using the quotient rule of exponents, we can simplify the expression step by step. Let's break it down:

The given expression is (2^8) / (2^4) = 32 / (2^2) / (2^12) / (2^3).

To simplify:

Step 1: Apply the quotient rule of exponents.
When dividing two terms with the same base, subtract their exponents: 2^8 / 2^4 = 2^(8-4) = 2^4.

So, the expression becomes 2^4 = 32 / (2^2) / (2^12) / (2^3).

Step 2: Simplify the terms inside the divisions.
Simplify 32 / (2^2) to get 32 / 4 = 8.

Now, the expression becomes 2^4 = 8 / (2^12) / (2^3).

Step 3: Simplify the remaining divisions.
Apply the quotient rule of exponents again:
8 / (2^12) = 8 / (2^(12-4)) = 8 / (2^8).

Now, the expression becomes 2^4 = 8 / (2^8) / (2^3).

Step 4: Simplify the divisions once more
Apply the quotient rule of exponents one last time:
8 / (2^8) = 8 / (2^(8-3)) = 8 / (2^5) = 8 / 32 = 1/4.

Finally, we have:
2^4 = 1/4.

Therefore, an equivalent form using the quotient rule of exponents is 2^4 = 1/4.