Question

Write each expression without the radical.

open the picture.

Answer 1

Answer:

Part 1) $4m^{\frac{1}{2}}$

Part 2) $3(r)^{\frac{1}{3}}(s)^{\frac{2}{3}}(t)^{\frac{4}{3}}$

Part 3) $3(x)^{\frac{9}{4}}$

Step-by-step explanation:

Part 1) Write each expression without the radical.

we have

$\sqrt{16m}$

we know that

$16=4^2$

substitute

$\sqrt{4^2m}$

Remember that

$\sqrt[a]{x^b}=x^{\frac{b}{a}}$

$(x^a)^{b}=x^{ab}$

so

$\sqrt{4^2m}=(4^2m)^{\frac{1}{2}}=(4^2)^{\frac{1}{2}}(m)^{\frac{1}{2}}=4m^{\frac{1}{2}}$

Part 2) Write each expression without the radical.

we have

$\sqrt[3]{27rs^2t^4}$

we know that

$27=3^3$

substitute

$\sqrt[3]{3^3rs^2t^4}$

Remember that

$\sqrt[a]{x^b}=x^{\frac{b}{a}}$

$(x^a)^{b}=x^{ab}$

so

$\sqrt[3]{3^3rs^2t^4}=(3^3rs^2t^4)^{\frac{1}{3}}=(3^3)^{\frac{1}{3}}(r)^{\frac{1}{3}}(s^2)^{\frac{1}{3}}(t^4)^{\frac{1}{3}}=3(r)^{\frac{1}{3}}(s)^{\frac{2}{3}}(t)^{\frac{4}{3}}$

Part 3) Write each expression without the radical.

we have

$\sqrt[4]{81x^9}$

we know that

$81=3^4$

substitute

$\sqrt[4]{3^4x^9}$

Remember that

$\sqrt[a]{x^b}=x^{\frac{b}{a}}$

$(x^a)^{b}=x^{ab}$

so

$\sqrt[4]{3^4x^9}=(3^4x^9)^{\frac{1}{4}}=(3^4)^{\frac{1}{4}}(x^9)^{\frac{1}{4}}=3(x)^{\frac{9}{4}}$