4 years ago

I need help! thank you!

Mathematics

1 answer:

denis-greek [22]4 years ago

7 0

Answer:

Step-by-step explanation:

1)b ^3 ×b ^6 =b ^(3+6) =b ^9

2) 5 ^2 ×5 ^4 =5 ^(2+4) =5 ^6

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ANSWER

$3 {x}^{2} y \sqrt[4]{y}$

EXPLANATION

We want to simplify:

$\sqrt[4]{81 {x}^{8} {y}^{5} }$

We can split the radical sign to obtain:

$\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{5} }$

$\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4} \times y}$

$\sqrt[4]{81} \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}$

$\sqrt[4]{ {3}^{4} } \times \sqrt[4]{ {x}^{8} } \times \sqrt[4]{ {y}^{4}} \times \sqrt[4]{y}$

Recall that:

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

${3}^{4 \times \frac{1}{4} } \times {x}^{8 \times \frac{1}{4} } \times {y}^{4 \times \frac{1}{4} }\times \sqrt[4]{y}$

$3 {x}^{2} y \sqrt[4]{y}$

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4 years ago

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