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Simplify (6x^−2)^2(0.5x)^4
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To simplify (6x^−2)^2(0.5x)^4, we can first simplify each term separately and then multiply them together.
First, let's simplify (6x^−2)^2. Using the exponent properties, we can rewrite it as 6^2(x^−2)^2.
Simplifying 6^2 gives us 36.
Simplifying (x^−2)^2 means squaring the exponent and distributing it to the base, which gives us x^−4.
So, (6x^−2)^2 simplifies to 36x^−4.
Next, let's simplify (0.5x)^4. Using the exponent properties, we can rewrite it as 0.5^4(x)^4.
Simplifying 0.5^4 gives us 0.0625.
Simplifying (x)^4 simply means raising x to the power of 4.
So, (0.5x)^4 simplifies to 0.0625x^4.
Finally, let's multiply the simplified terms together:
36x^−4 * 0.0625x^4 = 2.25x^4 * x^−4 using the product of powers property.
Combining the x terms gives us 2.25x^(4 + -4), which simplifies to 2.25.
Therefore, (6x^−2)^2(0.5x)^4 simplifies to 2.25.