Question

What expression is equivalent to 25 X 9y3

Answer 1

Answer:

D

Step-by-step explanation:

Use exponents property:

$\dfrac{x^a}{x^b}=x^{a-b}$

1. Note that

$\dfrac{x^9}{x^6}=x^{9-6}=x^3$

and

$\dfrac{y^3}{y^{11}}=y^{3-11}=y^{-8}=\dfrac{1}{y^8}$

2. Now

$\sqrt{25}=5\\ \\\sqrt{64}=8\\ \\\sqrt{x^3}=x\sqrt{x}\\ \\\sqrt{\dfrac{1}{y^8}}=\dfrac{1}{y^4}$

So

$\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}=\dfrac{\sqrt{25}\sqrt{x^3}}{\sqrt{64}\sqrt{y^8}}=\dfrac{5x\sqrt{x}}{8y^4}$

because $x>0,\ y>0$

Answer 2

Answer: Last option.

Step-by-step explanation:

You need to remember the Quotient of powers property:

$\frac{a^m}{a^n}=a^{(m-n)}$

 Applying this property, we know that:

$\sqrt{\frac{25x^9y^3}{64x^6y^{11}} }=\sqrt{\frac{25x^3}{64y^8}}$

Descompose 25 and 64 into their prime factors:

$25=5*5=5^2\\64=8*8=8^2$

Since:

$\sqrt[n]{a^n}=a$

And according to the Product of powers property:

$(a^m)(a^n)=a^{(m+n)}$

You can simplify. So, the equivalent expression is:

$\sqrt{\frac{5^2x^2*x}{8^2y^8}}=\frac{5x\sqrt{x} }{8y^4}$