Question

What is the simplified form of
72x16
50x36
? Assume x+0.
6
5x10
6
5x2
10

Answer 1

Answer:

The simplified form is  $\frac{6}{5x^{10} }$ ⇒ A

Step-by-step explanation:

• To simplify a root divide the power of the variable by 2 to cancel it

• Factorize the coefficient of the variable and take out the repeated factor twice out the root

Let us solve the question

∵ The expression is $\sqrt{\frac{72x^{16}}{50x^{36}}}$

→ At first, divide simplify the coefficient of the variable

∵ $\frac{72}{50}=\frac{36}{25}$

∵ 36 = 6 × 6 and 25 = 5 × 5

→ 6 and 5 repeated twice then the can go out the root one 6 and one 5

∴ $\sqrt{\frac{36}{25}}=\frac{6}{5}$

→ Let us use the exponent rule with division $\frac{a^{m} }{a^{n}}=a^{m-n}$

∵ $\frac{x^{16}}{x^{36}}=x^{(16-36)}=x^{-20}$

→ To cancel the root divide the power by 2

∵ -20 ÷ 2 = -10

∴ $\sqrt{x^{-20}}=x^{-10}$

∴  $\sqrt{\frac{72x^{16}}{50x^{36}}}$ = $\frac{6}{5}$ × $x^{-10}$

→ To change the power of x from (-) to (+) reciprocal x

∴ $x^{-10}=\frac{1}{x^{10}}$

∴  $\sqrt{\frac{72x^{16}}{50x^{36}}}$ = $\frac{6}{5x^{10} }$

∴ The simplified form is  $\frac{6}{5x^{10} }$