Question
Simplify (6x^-2)^2 (0.5x)^4
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GPT 3.5
To simplify the expression (6x^-2)^2 (0.5x)^4, we can first simplify each term separately and then multiply them together.
For the first term, (6x^-2)^2:
Squaring the 6 gives 6^2 = 36.
To square x with a negative exponent of -2, we can rewrite it as 1/x^2.
So, (6x^-2)^2 = (36 * (1/x^2))^2 = (36/x^2)^2 = (36^2)/(x^2)^2 = 1296/x^4.
For the second term, (0.5x)^4:
Raising 0.5x to the power of 4 gives (0.5x)^4 = (0.5^4) * (x^4) = 0.0625x^4.
Now, multiplying the simplified terms together:
(6x^-2)^2 (0.5x)^4 = (1296/x^4) * (0.0625x^4) = (1296 * 0.0625) * (x^-4 * x^4) = 81 * 1 = 81.
Therefore, the simplified expression is 81.
For the first term, (6x^-2)^2:
Squaring the 6 gives 6^2 = 36.
To square x with a negative exponent of -2, we can rewrite it as 1/x^2.
So, (6x^-2)^2 = (36 * (1/x^2))^2 = (36/x^2)^2 = (36^2)/(x^2)^2 = 1296/x^4.
For the second term, (0.5x)^4:
Raising 0.5x to the power of 4 gives (0.5x)^4 = (0.5^4) * (x^4) = 0.0625x^4.
Now, multiplying the simplified terms together:
(6x^-2)^2 (0.5x)^4 = (1296/x^4) * (0.0625x^4) = (1296 * 0.0625) * (x^-4 * x^4) = 81 * 1 = 81.
Therefore, the simplified expression is 81.
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