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AURORKA [14]
3 years ago
5

Simplify 3√875x⁵y⁹

Mathematics
2 answers:
taurus [48]3 years ago
8 0

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.

Alborosie3 years ago
7 0

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}}.

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