Is the product rule of exponents to simplify the expression 2√4 . 2√2
No, the product rule of exponents is used to simplify expressions involving exponentiation, not expressions involving square roots. The product rule of exponents states that when you multiply two numbers with the same base, you add their exponents. In this case, you would add the exponents of 2 in the expressions 2√4 and 2√2. However, since square roots are not exponents, the product rule of exponents does not apply.
No, the product rule of exponents is not used to simplify the expression 2√4 . 2√2.
The expression 2√4 . 2√2 can be simplified by using the distributive property of multiplication over addition.
First, we can simplify each square root individually:
√4 = 2
√2 = √2
Then, we can multiply the simplified values:
2√4 . 2√2 = (2)(2)√4√2
Using the properties of square roots (√a * √b = √(a * b)), we can simplify further:
(2)(2)√4√2 = 4√(4 * 2)
Finally, simplifying the remaining square root:
4√(4 * 2) = 4√8
The expression 2√4 . 2√2 can be simplified to 4√8.