Question

Simplify 3√875x⁵y⁹

Answer 1

Answer:

5∛7 × $x^{5/3}$ × y³ is answer.

Step-by-step explanation:

we have to simplify the given expression 3√875x⁵y⁹

we use exponent rule for radical   $\sqrt[n]{xy} = \sqrt[n]{x} \sqrt[n]{y}$

we use this rule is this expression

3√875x⁵y⁹ = ∛875 × ∛x⁵ × ∛y⁹

∛875 = ∛125 ×7 = 5 ∛ 7

using exponent rule for radical $\sqrt[n]{x^{m}}=x^{m/n}$ we get

$\sqrt[3]{x^{5} } =x^{5/3}$

similarly

$\sqrt[3]{y^{9} } = y^{9/3}$

putting these values in given expression we get

3√875x⁵y⁹ =  5∛7 × $x^{5/3}$ × y³

therefore, our expression simplifies to 5∛7 ×$x^{5/3}$ × y³.

Answer 2

Answer:

$5\sqrt[3]{7}*y^3*x^{\frac{5}{3}}$

Step-by-step explanation:

We are asked to simplify the radical expression: $\sqrt[3]{875x^5y^9}$.

Using exponent rule for radical $\sqrt[n]{ab} =\sqrt[n]{a}*\sqrt[n]{b}$ we can rewrite our expression as:

$\sqrt[3]{875x^5y^9}=\sqrt[3]{875}*\sqrt[3]{x^5}*\sqrt[3]{y^9}$

$\sqrt[3]{875}=\sqrt[3]{125*7}=5\sqrt[3]{7}$

Using exponent rules for radical $\sqrt[n]{a^m}=a^\frac{m}{n}$ we will get,

$\sqrt[3]{x^5}=(x^5)^{\frac{1}{3}}=x^{\frac{5}{3}}$

Using exponent rules for radical $\sqrt[n]{a^m}=a^\frac{m}{n}$ we will get,

$\sqrt[3]{y^9}=(y^9)^3=y^{\frac{9}{3}}=y^3$

Upon substituting these values in our expression we will get,

$\sqrt[3]{x^5}*\sqrt[3]{y^9}=5\sqrt[3]{7}*x^{\frac{5}{3}}*y^3$

Therefore, our radical expression simplifies to $5\sqrt[3]{7}*y^3*x^{\frac{5}{3}}$.