Identify Components: Identify the components of the expression.We have the square root of 75 times b raised to the 10th power, which is written as 75b10.
Prime Factorization of 75: Break down the square root into prime factors for the number 75.75 can be factored into 3×25, and 25 is a perfect square (5×5).So, 75=3×52.
Simplify Perfect Square: Simplify the square root of the perfect square.Since 52 is a perfect square, its square root is 5.So, 52=5.
Apply Square Root to Variable: Apply the square root to the variable with an even exponent.The exponent of b is 10, which is an even number. The square root of b10 is b raised to the power of 210, which is b5.So, b10=b5.
Combine Simplified Components: Combine the simplified components.We have 3 which cannot be simplified further, 5 from the square root of 25, and b5 from the square root of b10.So, the simplified form is 5×b5×3.
More problems from Evaluate integers raised to positive rational exponents