Question
Simplify (6x^-2)^2(0.5x)^4 show work
Answers
GPT 3.5
To simplify (6x^-2)^2(0.5x)^4, we first need to simplify the exponent terms.
For (6x^-2)^2, we square both the coefficient and the variable separately:
(6^2)(x^-2)^2 = 36(x^-4)
Similarly, for (0.5x)^4, we raise the coefficient and the variable separately to the power of 4:
(0.5^4)(x^4) = 0.0625(x^4)
Now we can simplify further:
36(x^-4) * 0.0625(x^4) = 2.25(x^0)
Since any number raised to the power of 0 is equal to 1, we have:
2.25(x^0) = 2.25
Therefore, the simplified form of (6x^-2)^2(0.5x)^4 is 2.25.
For (6x^-2)^2, we square both the coefficient and the variable separately:
(6^2)(x^-2)^2 = 36(x^-4)
Similarly, for (0.5x)^4, we raise the coefficient and the variable separately to the power of 4:
(0.5^4)(x^4) = 0.0625(x^4)
Now we can simplify further:
36(x^-4) * 0.0625(x^4) = 2.25(x^0)
Since any number raised to the power of 0 is equal to 1, we have:
2.25(x^0) = 2.25
Therefore, the simplified form of (6x^-2)^2(0.5x)^4 is 2.25.