Question

Which expression is equivalent to √128x^5y^6/2x^7y^5? Assume x>0 and y>0.

Answer 1

Answer:

The correct option is D.

Step-by-step explanation:

The given expression is,

$\sqrt{\frac{128x^5y^6}{2x^7y^5}}$

$\sqrt{\frac{64x^5y^6}{x^7y^5}}$

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$,

$\sqrt{64x^{5-7}y^{6-5}}$

$\sqrt{64x^{-2}y^{6-5}}$

Use exponent rule $a^{-n}=\frac{1}{a^n}$,

$\sqrt{64\times \frac{1}{x^2}\times y}$

$\sqrt{(\frac{8}{x})^2\times y}$

$\frac{8\sqrt{y}}{x}$

Therefore option D is correct.

Answer 2

$\sqrt{\dfrac{128x^5y^6}{2x^7y^5}}=\sqrt{\dfrac{128}{2}\cdot\dfrac{x^5}{x^7}\cdot\dfrac{y^6}{y^5}}=\sqrt{64\cdot\dfrac{1}{x^2}\cdot y}=\sqrt{64}\cdot\sqrt{\dfrac{1}{x^2}}\cdot\sqrt{y}=\\\\\\=8\cdot\dfrac{1}{x}\cdot\sqrt{y}=\boxed{\dfrac{8\sqrt{y}}{x}}$

Answer D.