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

Answer:
The simplified form is [tex]\frac{6}{5x^{10} }[/tex] ⇒ A
Step-by-step explanation:
Let us solve the question
∵ The expression is [tex]\sqrt{\frac{72x^{16}}{50x^{36}}}[/tex]
→ At first, divide simplify the coefficient of the variable
∵ [tex]\frac{72}{50}=\frac{36}{25}[/tex]
∵ 36 = 6 × 6 and 25 = 5 × 5
→ 6 and 5 repeated twice then the can go out the root one 6 and one 5
∴ [tex]\sqrt{\frac{36}{25}}=\frac{6}{5}[/tex]
→ Let us use the exponent rule with division [tex]\frac{a^{m} }{a^{n}}=a^{m-n}[/tex]
∵ [tex]\frac{x^{16}}{x^{36}}=x^{(16-36)}=x^{-20}[/tex]
→ To cancel the root divide the power by 2
∵ -20 ÷ 2 = -10
∴ [tex]\sqrt{x^{-20}}=x^{-10}[/tex]
∴ [tex]\sqrt{\frac{72x^{16}}{50x^{36}}}[/tex] = [tex]\frac{6}{5}[/tex] × [tex]x^{-10}[/tex]
→ To change the power of x from (-) to (+) reciprocal x
∴ [tex]x^{-10}=\frac{1}{x^{10}}[/tex]
∴ [tex]\sqrt{\frac{72x^{16}}{50x^{36}}}[/tex] = [tex]\frac{6}{5x^{10} }[/tex]
∴ The simplified form is [tex]\frac{6}{5x^{10} }[/tex]