Multiply - -27a3b2c4- 3 128a7b9c2- 6 729ab12c2

√(27a^3b^2c^4)√(128a^7b^9c^2)√(729ab^12c^2) ———————————————— √(27a^3b^2c^4)=3√(3)bc^2a^3/2 —————————————————– √(128a^7b^9c^2)=4√(2)b^3√(a^7c^2) —— ...

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Byju's Answer

Standard VII

Mathematics

Exponents with Unlike Bases and Same Exponent

Multiply - √...

Question

Multiply -
$\sqrt{27 a^{3} b^{2} c^{4}} \times \sqrt[3]{128 a^{7} b^{9} c^{2}} \times \sqrt[6]{729 a b^{12} c^{2}}$

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Solution

$\sqrt{27 a^{3} b^{2} c^{4}} \sqrt[3]{128 a^{7} b^{9} c^{2}} \sqrt[6]{729 a b^{12} c^{2}}$

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$\sqrt{27 a^{3} b^{2} c^{4}} = 3 \sqrt{3} b c^{2} a^{\frac{3}{2}}$

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$\sqrt[3]{128 a^{7} b^{9} c^{2}} = 4 \sqrt[3]{2} b^{3} \sqrt[3]{a^{7} c^{2}}$

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$\sqrt[6]{729 a b^{12} c^{2}} = 3 b^{2} \sqrt[6]{a c^{2}}$

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$= 3 \sqrt{3} b c^{2} a^{\frac{3}{2}} \cdot 4 \sqrt[3]{2} b^{3} a^{\frac{7}{3}} c^{\frac{2}{3}} \cdot 3 b^{2} \sqrt[6]{a} \sqrt[3]{c}$

$= 4 \sqrt[3]{2} \cdot 3^{\frac{5}{2}} b^{3} b^{2} b c^{2} a^{\frac{3}{2}} a^{\frac{7}{3}} \sqrt[6]{a} c^{\frac{2}{3}} \sqrt[3]{c}$

$= 4 \sqrt[3]{2} \cdot 3^{\frac{5}{2}} a^{4} b^{3} b^{2} b c^{2} c^{\frac{2}{3}} \sqrt[3]{c}$

$= 4 \sqrt[3]{2} \cdot 3^{\frac{5}{2}} a^{4} b^{6} c^{2} c^{\frac{2}{3}} \sqrt[3]{c}$

$= 4 \sqrt[3]{2} \cdot 3^{\frac{5}{2}} a^{4} b^{6} c^{3}$

$= 3^{2} \cdot 4 \sqrt[3]{2} \sqrt{3} a^{4} b^{6} c^{3}$

$= 36 \sqrt[3]{2} \sqrt{3} (a^{4} b^{6} c^{3})$

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Similar questions

Q. Verify that

27 a^{3} + b^{3} + c^{3} - 9 a b c = (3 a + b + c) [9 a^{2} + b^{2} + c^{2} - 3 a b - b c - 3 a c]

Q. In

△ A B C

2 a^{2} b^{2} + 2 b^{2} c^{2} = a^{4} + b^{4} + c^{4}, ∠ B =

Q. Simplify:

\frac{a^{2} - {(b - c)}^{2}}{{(a + c)}^{2} - b^{2}} + \frac{b^{2} - {(a - c)}^{2}}{{(a + b)}^{2} - c^{2}} + \frac{c^{2} - {(a - b)}^{2}}{{(b + c)}^{2} - a^{2}}

Q. If a,b,c are in continued proportion prove that :
i)

\frac{a^{2} + a b + b^{2}}{b^{2} + b c + c^{2}} = \frac{a}{c}

.
ii)

\frac{a^{4} + a^{2} b^{2} + b^{4}}{b^{4} + b^{2} c^{2} + c^{4}} = \frac{a^{2}}{c^{2}}

Q. If in a

△ A B C, a^{4} + b^{4} + c^{4} = 2 a^{2} b^{2} + b^{2} c^{2} + 2 c^{2} a^{2},

then

sin A

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Multiply -√27a3b2c4×3√128a7b9c2×6√729ab12c2

Multiply -
$\sqrt{27 a^{3} b^{2} c^{4}} \times \sqrt[3]{128 a^{7} b^{9} c^{2}} \times \sqrt[6]{729 a b^{12} c^{2}}$