Write an equivalent expression using radical notation

1.(a^2b^2)^1/9

Use the laws of exponents to simplify
2.6^3/5* 6^5/10

1. a^(2/9) * b^(2/9)

2. 6^[(3/5) + (5/10)] = 6^(11/10) = 6^1.1

rewrite the expression using radical notation. 2 1/3

1. To write an equivalent expression using radical notation for (a^2b^2)^1/9, we need to remember that raising a number or expression to the power of 1/n is equivalent to taking the nth root of that number or expression. Therefore, we can rewrite (a^2b^2)^1/9 as the ninth root of (a^2b^2).

In radical notation, the equivalent expression would be:
∛(a^2b^2)

2. To simplify 6^3/5 * 6^5/10 using the laws of exponents, we can use the rule that when you multiply two numbers with the same base, you add their exponents.

So, we have:
6^3/5 * 6^5/10 = 6^(3/5 + 5/10)

To add the exponents with different denominators, we need a common denominator. In this case, the common denominator is 10. Therefore:
6^(3/5 + 5/10) = 6^(6/10 + 5/10)

Now, we can simplify the sum of the exponents:
6^(6/10 + 5/10) = 6^(11/10)

So, the simplified expression is 6^(11/10).