Question

Which expression is equal to four to the power of 5 × 4 To the power of -7 ÷ 4 to the power of -2

Answer 1

To simplify the expression, we can use the exponent rule that states:
a^m × a^n = a^(m+n)
Additionally, the rule a^m ÷ a^n = a^(m-n) can be used.

Using the first rule, we can combine the exponents when multiplying.
And using the second rule, we can subtract the exponents when dividing.

Given that:
4^5 × 4^(-7) ÷ 4^(-2)

Let's start multiplying:
4^5 × 4^(-7) = 4^(5 + (-7))
= 4^(-2)

Next, divide:
4^(-2) ÷ 4^(-2) = 4^(-2 - (-2))
= 4^(0)

The expression simplifies to 4^0.

Any number (except zero) raised to the exponent of zero is equal to 1.
Therefore, 4^0 = 1.

Hence, the expression is equal to 1. Answer: \boxed{1}.