Math  /  Algebra

Question11) 12+x4612+x^{4}-6 when x=8x=8

Studdy Solution

STEP 1

What is this asking? We need to substitute x=8x = 8 into the expression 12+x4612 + x^4 - 6 and calculate the result. Watch out! Don't forget the order of operations—we need to handle the exponent before adding or subtracting!

STEP 2

1. Simplify the expression
2. Substitute and calculate

STEP 3

First, let's **simplify** our expression.
We've got 12+x4612 + x^4 - 6.
Notice we can combine the **constant terms** 1212 and 6-6.
We have 126=612 - 6 = 6, so our simplified expression is x4+6x^4 + 6.
This makes our calculation easier!

STEP 4

Now, let's **substitute** our value of x=8x = 8 into the simplified expression: x4+6x^4 + 6 becomes 84+68^4 + 6.

STEP 5

Remember, 848^4 means 88 multiplied by itself four times: 88888 \cdot 8 \cdot 8 \cdot 8.
Let's break it down: 88=648 \cdot 8 = 64, then 648=51264 \cdot 8 = 512, and finally 5128=4096512 \cdot 8 = 4096.
So, 84=40968^4 = \textbf{4096}.

STEP 6

Now, we just need to add 66 to our result: 4096+6=41024096 + 6 = \textbf{4102}.

STEP 7

Our **final answer** is 41024102!

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