Question

. Express the radical form (15/21)^2/5​

Answer 1

Question :-

Express the radical form of :

 $\sf \bigg(\dfrac{15}{21} \bigg)^{\frac{2}{5} }$

Answer :-

Concept :

Radical is the (√) symbol that is used to denote the square root. Radical expression refers to an expression containing a radical. Radicand refers to a expression inside the radical.

Solution :-

By using the exponent laws,

• $\to \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{a^{m}}{b^{m}}$

$\implies \dfrac{15^{\frac{2}{5} }}{21^{\frac{2}{5} }}$

• $\to (a^{m})^{n} = a^{m\timesn}$

$\implies \sf \dfrac{(15)^{2\times \frac{1}{5}} }{(21)^{2\times\frac{1}{5} }}$

Finding the square of 15 and 21 respectively,

$\implies \sf \dfrac{225^{\frac{1}{5} }}{441^{\frac{1}{5} }}$

$\to a^{\frac{1}{n}}= \sqrt[n]{a}$

$\implies \sf \dfrac{\sqrt[5]{225} }{\sqrt[5]{441} }$

$\to \dfrac{a^{m}}{b^{m}} =\bigg( \dfrac{a}{b}\bigg) ^{m}$

$\implies \sf \sqrt[5]{\dfrac{225}{441} }$

Hence, the radical form of $\sf \bigg(\dfrac{15}{21} \bigg)^{\frac{2}{5} }$ is $\implies \sf \sqrt[5]{\dfrac{225}{441} }$

Important points to note :-

• aⁿ × aᵇ = aⁿ⁺ᵇ
• aⁿ × bⁿ = abⁿ
• a⁻ⁿ = 1/aⁿ
• aⁿ ÷ aᵇ = aⁿ⁻ᵇ
• $\boxed {\begin\longrightarrow \sf a^{m} \times a^{n} = a^{m+n} \\ \longrightarrow \sf a^{m} \div a^{n} = a^{m-n} \\ \longrightarrow \sf a^{m} \times b^{m} = (ab)^{m} \\ \longrightarrow \sf \dfrac{a^{m}}{b^{m}} = \bigg(\dfrac{a}{b} \bigg)^{m} \\ \longrightarrow \sf a^{-m} = \dfrac{1}{a^{m}} \\ \longrightarrow \sf a^{0} = 1 \\ \longrightarrow \sf a^{\frac{1}{n} }= \sqrt[n]{a}\end}$(aⁿ/bⁿ) = (a/b)ⁿ
• a⁰ = 1
• $\sf a^{\frac{1}{n} }= \sqrt[n]{a}$

Answer 2

Answer:

Here is your answer

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Step-by-step explanation:

(15/21)^2/5

=(15^2)/(21^2)^5

=225/441^5