Math Snap

STEP 1

Assumptions1. The base of all the expressions is4. The laws of exponents apply, which are a. $a^{m} \times a^{n} = a^{m+n}$
b. $\frac{a^{m}}{a^{n}} = a^{m-n}$
c. $a^{-n} = \frac{1}{a^{n}}$

STEP 2

We start by simplifying the given expression using the laws of exponents. The expression is $4^{5} \times4^{-7} \div4^{-2}$.

STEP 3

First, we can simplify the multiplication and division operations using the laws of exponents. According to the law $a^{m} \times a^{n} = a^{m+n}$ and $\frac{a^{m}}{a^{n}} = a^{m-n}$, we can add the exponents when multiplying and subtract the exponents when dividing.
$$^{5} \times^{-7} \div^{-2} =^{5 + (-7) - (-2)}$$

STEP 4

implify the expression inside the parentheses.
$$4^{ + (-7) - (-2)} =4^{ -7 +2}$$

STEP 5

Perform the operations inside the parentheses.
$$4^{5 -7 +2} =4^{0}$$

By the law of exponents, any number raised to the power of0 is1. Therefore, the expression simplifies to1.
$$4^{0} =1$$Therefore, the expression $4^{5} \times4^{-} \div4^{-2}$ is equal to $4^{0}$.