Final answer:
The expression 8√63x^14y^9 simplifies to 24x^7y^4.5√7 by taking the principal square roots of 63, x^14 and y^9 and multiplying by 8.
Step-by-step explanation:
To simplify 8√63x^14y^9, we need to break down the number under the square root into its principal square factors and simplify the powers of the variables.
Firstly, let's simplify the square root number:
The square root of 63 can be broken down into √(9x7). We can then simplify √9 into 3. So, we're left with 3√7.
Next, we simplify the variables with powers:
For x^14, the principal square root would be x^(14/2), which simplifies to x^7. Similarly, for y^9, the principal square root would be y^(9/2). However, since 9 is an odd number, we cannot simplify it further into a whole number and we get y^(4.5).
Therefore, the simplified version of 8√63x^14y^9 is 24x^7y^4.5√7.
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