Let's simplify the expression [tex]\( 4^{-4} \)[/tex].
Step 1: Understand the negative exponent.
A negative exponent means that we take the reciprocal of the base raised to the absolute value of the exponent. So, [tex]\( 4^{-4} \)[/tex] can be written as:
[tex]\[ 4^{-4} = \frac{1}{4^4} \][/tex]
Step 2: Calculate the value of [tex]\( 4^4 \)[/tex].
We need to calculate [tex]\( 4^4 \)[/tex], which means multiplying the number 4 by itself 4 times:
[tex]\[ 4^4 = 4 \times 4 \times 4 \times 4 \][/tex]
Step 3: Perform the multiplication.
[tex]\[ 4 \times 4 = 16 \][/tex]
[tex]\[ 16 \times 4 = 64 \][/tex]
[tex]\[ 64 \times 4 = 256 \][/tex]
Thus,
[tex]\[ 4^4 = 256 \][/tex]
Step 4: Write the reciprocal.
Now, substitute [tex]\( 4^4 \)[/tex] back into the reciprocal from step 1:
[tex]\[ 4^{-4} = \frac{1}{4^4} = \frac{1}{256} \][/tex]
Therefore, the simplified value of [tex]\( 4^{-4} \)[/tex] is:
[tex]\[ \frac{1}{256} \][/tex]
