Can anyone show me how to simplify this step-by-step? THANKS A MILLION!
(6x^-2)^2(0.5x)^4
I thought this question looked familiar.
Did it on Friday
http://www.jiskha.com/display.cgi?id=1455295033
x ^ - 2 = 1 / x ^ 2
( 6 x ^ - 2 ) ^ 2 =
( 6 / x ^ 2 ) ^ 2 =
6 ^ 2 / ( x ^ 2 ) ^ 2 =
36 / x ^ 4
( 0.5 x ) ^ 4 =
0.5 ^ 4 * x ^ 4 =
0.0625 x ^ 4
( 6 x ^ - 2 ) ^ 2 0.5 x ^ 4 =
( 36 / x ^ 4 ) * 0.0625 x ^ 4 =
36 * 0.0625 * x ^ 4 / x ^ 4 =
36 * 0.0625 = 2.25
Thanks guys! I owe you one!
Of course! I'd be happy to help you simplify the expression step-by-step.
The expression you provided is:
(6x^-2)^2(0.5x)^4
To simplify it, we'll start by simplifying the individual terms within the parentheses.
Step 1: Simplify (6x^-2) squared
To square (6x^-2), we need to multiply it by itself:
(6x^-2)(6x^-2)
To multiply two terms with the same base (x), we add their exponents together. So, we add the exponents of 6x and -2:
6^2 * x^-2 * x^-2
Now we can simplify the numerical part:
36 * x^-2 * x^-2
Step 2: Simplify (0.5x) raised to the power of 4
To raise (0.5x) to the power of 4, we need to multiply it by itself four times:
(0.5x)(0.5x)(0.5x)(0.5x)
Again, we can simplify the numerical part:
0.5^4 * x^4
Now, we have simplified the expression to:
36 * x^-2 * x^-2 * 0.5^4 * x^4
Step 3: Combine the like terms
To combine like terms, we can add or subtract their coefficients and keep the same base (x). Here, the like terms have the base x:
36 * x^-2 * x^-2 * 0.5^4 * x^4
Now we can simplify the exponents by adding them together:
36 * x^(-2-2) * 0.5^4 * x^4
Simplifying further, we have:
36 * x^-4 * 0.5^4 * x^4
Lastly, we can simplify the numerical part:
36 * 0.0625 * x^(4-4)
Since x^(4-4) equals x^0, which is equal to 1, the final simplified expression is:
36 * 0.0625 * 1
Multiplying the numerical coefficients:
2.25
Therefore, the simplified expression is 2.25.
I hope this step-by-step explanation helps! If you have any more questions, feel free to ask.