Question

Complete the steps to simplify (y^4/3•y^2/3)^-1/2. Apply the product of powers property to the expression inside the parentheses, then choose the equivalent expression.
A. (y^2)^-1/2
B. (y^8/3)^-1/2
C. (y^2/3)^-1/2

Answer 1

Option A

$\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}$

Solution:

Given expression is:

$\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}$

Product of powers property:

The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents

Which is represented as,

$a^m.a^n = a^{m+n}$

Therefore, the given expression becomes,

$\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}$

Now add the exponents, we get

$\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}$

Simplify the above expression

$\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}$

Simplify the exponent of y, we get

$\left(y^{2}\right)^{\frac{-1}{2}}$

Thus Option A is correct

Answer 2

Answer:

The answer is A

Step-by-step explanation: