Mathematics: Which expression is equivalent to ^3 √1/1000c^9d^12 1/100c^3d^4 1/100c^6d^9 1/10c^3d^4 1/10c^6d^9

Which expression is equivalent to ^3 √1/1000c^9d^12

Ответ:

ykpwincess

09.03.2022

Mathematics

$\frac{1}{10c^{3}d^{4} }$

Step-by-step explanation:

THE GIVEN EXPRESSION IS

$\sqrt[3]{\frac{1}{1000c^{9}d^{12} } }$

To simplify this expression, we just have to apply the cubic root to each part of the fraction, as follows

$\frac{\sqrt[3]{1} }{\sqrt[3]{1000c^{9} d^{12} } }$

Then, we solve each root. Remember that to solve roots of powers, we just need to divide the exponent of the power by the index of the root, as follows

$\frac{1}{10c^{\frac{9}{3} } d^{\frac{12}{3} } }$

Therefore, the equivalent expression is

$\frac{1}{10c^{3}d^{4} }$

So, the right answer is the third choice.

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Which expression is equivalent to ^3 √1/1000c^9d^12 1/100c^3d^4 1/100c^6d^9 1/10c^3d^4 1/10c^6d^9

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