The third power of sqrt of 5b^9. Can someone point out the steps for solving this problem. Thanks for your help in advance.

change b^9 to b^8*b

sqrt (5b^8*b)=b^4 sqrt5b

now cube all that.

b^12 (5b)sqrt5b

[sqrt(5 b^9]^3 = [(5 b^9)^(1/2)]^3

= 5^(3/2) * b^(9/2)
= 11.18034.. b^(9/2)

To find the third power of the square root of 5b^9, follow these steps:

Step 1: Rewrite the square root as an exponent expression.
√(5b^9) can be expressed as (5b^9)^(1/2).

Step 2: Apply the power rule of exponents to raise the entire expression to the power of 3.
((5b^9)^(1/2))^3.

Step 3: Multiply the exponents.
The exponent of the base 5b^9 is (1/2) * 3 = 3/2.

Step 4: Rewrite the expression with the new exponent.
((5b^9)^(3/2)).

Hence, the third power of the square root of 5b^9 is ((5b^9)^(3/2)).