Sure! Let's work through the given expression step-by-step without using slashes.
Starting expression:
(7 raised to the power of negative 4 divided by 8 raised to the power of 6) raised to the power of negative 2 times 7 raised to the power of negative 3 divided by 8 raised to the power of 9
Step 1: Apply the negative exponent to the term inside the parentheses.
Using the rule that (a/b) raised to the power of n = a raised to the power of n divided by b raised to the power of n:
(7 raised to the power of negative 4) raised to the power of negative 2 divided by (8 raised to the power of 6) raised to the power of negative 2
Step 2: Simplify each part.
First, simplify (7 raised to the power of negative 4) raised to the power of negative 2:
7 raised to the power of negative 4 times negative 2 equals 7 raised to the power of 8
Next, simplify (8 raised to the power of 6) raised to the power of negative 2:
8 raised to the power of 6 times negative 2 equals 8 raised to the power of negative 12
Putting this together, we have:
7 raised to the power of 8 divided by 8 raised to the power of negative 12
Step 3: Rewrite the negative exponent.
Rewrite 8 raised to the power of negative 12 as 1 divided by 8 raised to the power of 12:
7 raised to the power of 8 times 1 divided by 8 raised to the power of 12
So now, we have:
7 raised to the power of 8 times 1 divided by 8 raised to the power of 12
Step 4: Now incorporate the second part of the original expression.
Next, we need to multiply by (7 raised to the power of negative 3 divided by 8 raised to the power of 9):
Continuing from our expression, we multiply by:
7 raised to the power of negative 3 divided by 8 raised to the power of 9:
So, the expression now looks like:
(7 raised to the power of 8 times 1 divided by 8 raised to the power of 12) times (7 raised to the power of negative 3 divided by 8 raised to the power of 9)
Step 5: Combine everything.
We can combine the powers of 7 and the powers of 8:
Numerator: 7 raised to the power of 8 times 7 raised to the power of negative 3 equals 7 raised to the power of (8 plus negative 3) which simplifies to 7 raised to the power of 5.
Denominator: 8 raised to the power of 12 times 8 raised to the power of 9 equals 8 raised to the power of (12 plus 9) which simplifies to 8 raised to the power of 21.
Final expression:
7 raised to the power of 5 divided by 8 raised to the power of 21
Therefore, the correct answer is:
7 raised to the power of 5 over 8 raised to the power of 21
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