Write each expression in radical form.
1. (10n)^3/2
My answer: sqrt of 10n to the power of 3
Could it be simplified further to 10n times sqrt of 10n?
2. a^6/5
My answer: the fifth root of a to the power of 6
Could it be simplified further to "a" times the fifth root of "a"?
1. To write the expression (10n)^3/2 in radical form, we start by converting the exponent 3/2 into a radical. The exponent 3/2 represents the square root of the cube, so it can be written as a square root.
Therefore, (10n)^3/2 can be written as the square root of (10n)^3.
Simplifying this further, we can expand the cube inside the square root, giving us the square root of (10n * 10n * 10n).
This can be simplified to 10n times the square root of (10n).
2. To write the expression a^6/5 in radical form, we convert the exponent 6/5 into a radical. The exponent 6/5 represents the fifth root of the sixth power.
Therefore, a^6/5 can be written as the fifth root of a^6.
Simplifying this further, we can expand the sixth power inside the fifth root, giving us the fifth root of (a * a * a * a * a * a).
This can be simplified to "a" times the fifth root of "a".