Use the properties of exponents and radicals to generate an equivalent expression for (256√10)551213%0D%0A(%0D%0A256%0D%0A10%0D%0A)%0D%0A5%0D%0A512%0D%0A1%0D%0A3%0D%0A.
To generate an equivalent expression for (256√10)^551213 / (256 * 10)^(5 * 512)^(1/3), we can use the properties of exponents and radicals.
First, let's simplify the expression inside the parentheses (256√10)^551213. Taking the square root of 10 is the same as raising it to the power of 1/2, so we have (256 * 10^(1/2))^551213.
Using the property (a * b)^n = a^n * b^n, we can rewrite this as (256^551213) * (10^(1/2))^551213.
Now let's simplify (10^(1/2))^551213. Using the property (a^m)^n = a^(m * n), we can rewrite this as 10^(1/2 * 551213).
Since 1/2 * 551213 is an integer, we have 10^275606.5.
To simplify the expression inside the parentheses (256 * 10)^(5 * 512)^(1/3), we first calculate (5 * 512) = 2560.
Then, using the property (a * b)^n = a^n * b^n, we can rewrite the expression as (256^2560)^(1/3).
To simplify further, we can use the property (a^m)^n = a^(m * n), so we have 256^(2560/3).
Finally, to generate an equivalent expression for (256√10)^551213 / (256 * 10)^(5 * 512)^(1/3), we can combine all the simplified expressions:
(256^551213) * (10^275606.5) / 256^(2560/3).