Answer:
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Explanation:
To simplify the expression, "a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed," we can break it down step by step.
First, let's simplify the numerator, which is "a raised to the negative fourth power." When a number or variable is raised to a negative exponent, it can be rewritten as its reciprocal with a positive exponent. Therefore, "a raised to the negative fourth power" can be rewritten as 1 over "a raised to the fourth power" or 1/a^4.
Next, let's simplify the denominator, which is "quantity 2 times b squared end quantity all cubed." To simplify this expression, we need to cube both the numerator and denominator separately.
The numerator, "2 times b squared," remains the same when cubed, so it becomes 2b^2.
The denominator, "2 times b squared," cubed means multiplying it by itself three times: (2b^2) x (2b^2) x (2b^2). When we multiply these terms together, we get 8b^6.
Now, let's simplify the expression by dividing the numerator by the denominator:
(1/a^4) / (8b^6)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
(1/a^4) * (1 / (8b^6))
Multiplying the numerators and denominators together, we get:
1 / (a^4 * 8b^6)
Simplifying further, we have:
1 / (8a^4b^6)
Therefore, the simplified expression is:
1 over quantity 8 times a raised to the fourth power times b raised to the sixth power end quantity, which can also be written as:
1 / (8a^4b^6)