What is the simplified expression for 4 power 4 multiplied by 4 power 3 over 4 power 5?

To simplify the expression 4⁴ × 4³ ÷ 4⁵, we can use the properties of exponents.

The property states that when multiplying two powers with the same base, we add the exponents. Therefore, we can first simplify the numerator:

• 4⁴ × 4³ = 4^{4 + 3} = 4⁷

Now we have:

• 4⁷ ÷ 4⁵

Next, we use the property that states when dividing two powers with the same base, we subtract the exponents:

• 4⁷ ÷ 4⁵ = 4^{7 – 5} = 4²

Thus, the simplified expression is 4², which equals 16.

Therefore, the final answer is:

• 16