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(15root(5)(root( 28)(a))-7root(7)(root( 20)(a)))/(2root(35)(root(4)(a)))

$\frac{15 \sqrt[5]{\sqrt[28]{a}}-7 \sqrt[7]{\sqrt[20]{a}}}{2 \sqrt[35]{\sqrt[4]{a}}}$

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Multiplication with rational exponents

Full solution

Q.

\frac{15 \sqrt[5]{\sqrt[28]{a}}-7 \sqrt[7]{\sqrt[20]{a}}}{2 \sqrt[35]{\sqrt[4]{a}}}

Simplify Radicals Inside Roots: Step $1$ : Simplify the radicals inside the roots. $\newline$ We start by simplifying the inner radicals for each term. $\newline$ $\sqrt{28}a$ simplifies to $\sqrt{4\cdot7}a = 2\sqrt{7}a$ , $\newline$ $\sqrt{20}a$ simplifies to $\sqrt{4\cdot5}a = 2\sqrt{5}a$ , $\newline$ $\sqrt{4}a$ simplifies to $\sqrt{2\cdot2}a = 2\sqrt{a}$ .
Substitute Simplified Radicals: Step $2$ : Substitute the simplified radicals back into the expression. $\newline$ Replace the simplified values back into the original expression: $\newline$ (\(15\sqrt{ $5$ }( $2$ \sqrt{ $7$ }(a)) - $7$ \sqrt{ $7$ }( $2$ \sqrt{ $5$ }(a))) / ( $2$ \sqrt{ $35$ }( $2$ \sqrt{(a)})).
Distribute Coefficients Inside Roots: Step $3$ : Distribute the coefficients inside the roots. $\newline$ Multiply the coefficients by the numbers inside the roots: $\newline$ $(30\sqrt{5}(\sqrt{7}(a)) - 14\sqrt{7}(\sqrt{5}(a))) / (4\sqrt{35}(\sqrt{a})).$
Combine Like Terms: Step $4$ : Simplify the expression by combining like terms. $\newline$ Since there are no like terms to combine, we proceed to simplify the denominator: $\newline$ $4\sqrt{35}(\sqrt{(a)})$ simplifies to $4\sqrt{35a}$ .
Simplify Entire Expression: Step $5$ : Simplify the entire expression. $\newline$ Divide the numerator by the denominator: $\newline$ $(30\sqrt{5}(\sqrt{7}(a)) - 14\sqrt{7}(\sqrt{5}(a))) / 4\sqrt{35a}$ .

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