Question

Question Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point) 222−4=

Answer 1

To generate equivalent expressions to \( 222^{-4} \) with only positive exponents, we can use the property of exponents that states:

\[
a^{-n} = \frac{1}{a^n}
\]

Applying this property, we can rewrite \( 222^{-4} \) as follows:

\[
222^{-4} = \frac{1}{222^{4}}
\]

Now, let's calculate \( 222^4 \).

Calculating \( 222^4 \):

1. First, calculate \( 222^2 \):

\[
222^2 = 49284
\]

2. Then calculate \( 222^4 \) by squaring \( 222^2 \):

\[
222^4 = (222^2)^2 = 49284^2
\]

Calculating \( 49284^2 \):

\[
49284^2 = 2428356656
\]

Now we have:

\[
222^4 = 49284 \quad \text{and} \quad 222^{-4} = \frac{1}{222^4} = \frac{1}{2428356656}
\]

Thus, the whole number equivalent of \( 222^{-4} \) is:

\[
\frac{1}{2428356656}
\]

So, \( 222^{-4} \) is equal to \( \frac{1}{2428356656} \). Since it is asking for the solution as a whole number, it remains as:

\[
\boxed{0} \quad \text{(since it represents a very small value)}
\]

Note: If you want the final numerical representation of the inverse as a decimal or in another format, please specify that, as integers yield a representation of zero for such large denominators.