Which expression is NOT equal to a3×b5b9×a5−−−−√𝑎3×𝑏5𝑏9×𝑎5?A.1a×b21𝑎×𝑏2B.a−1b−2𝑎−1𝑏−2C.ab2−−−√𝑎𝑏2D.(ab2)−
Question
Which expression is NOT equal to
a^3×b^5 / √(b^9×a^5)?
A. 1/(a×b^2)
B. a^(-1)b^(-2)
C. √(ab^2)
D. (ab^2)^{-1}
Solution
The expression given is a3×b5b9×a5−−−−√𝑎3×𝑏5𝑏9×𝑎5.
First, let's simplify this expression.
The square root of a product is equal to the product of the square roots. Therefore, we can rewrite the expression as √(a3×b5) / √(b9×a5).
Next, we can simplify the square roots by taking the square root of each term separately.
This gives us √a3 × √b5 / √b9 × √a5.
The square root of a number raised to an exponent is equal to the number raised to half the exponent. Therefore, we can simplify this further to a3/2 × b5/2 / b9/2 × a5/2.
Now, we can simplify the expression by canceling out common terms.
This gives us a3/2-5/2 × b5/2-9/2 = a-1 × b-2.
Therefore, the expression simplifies to a-1b-2.
Comparing this with the answer choices, we can see that the expression is NOT equal to C. √ab2.
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