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strojnjashka [21]
3 years ago
15

Please please help thank you

Mathematics
1 answer:
Tcecarenko [31]3 years ago
7 0

Answer:

b-4^3

Step-by-step explanation:

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The answer for the question shown above is the first option: x^2(x^2)^1/4
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(6-3(cube root of 6)/(cube root of 9)
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For this case we must simplify the following expression:

\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}}

Multiplying the numerator and denominator by(\sqrt [3] {9}) ^ 2

\frac {6-3 \sqrt [3] {6}} {\sqrt [3] {9}} * \frac {(\sqrt [3] {9}) ^ 2} {(\sqrt [3] { 9}) ^ 2} =

We rewrite:

\frac {\frac {6-3 \sqrt [3] {6}} * (\sqrt [3] {9}) ^ 2} {\sqrt [3] {9} * (\sqrt [3] {9 }) ^ 2} =

By properties of powers we have that:

a ^ m * a ^ n = a ^ {m + n}\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {(\sqrt [3] {9}) ^ 3} =\\\frac {(6-3 \sqrt [3] {6}) * (\sqrt [3] {9}) ^ 2} {9} =

We rewrite, moving the exponent within the radical:

\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {9 ^ 2}} {9} =\\\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {81}} {9} =

We can rewrite3 * 3 ^ 3 = 81

\frac {(6-3 \sqrt [3] {6}) * \sqrt [3] {3 * 3 ^ 3}} {9} =

We simplify:

\frac {(6-3 \sqrt [3] {6}) * 3 \sqrt [3] {3}} {9} =

We apply distributive property:

\frac {18 \sqrt [3] {3} -9 \sqrt [3] {18}} {9} =

Simplifying we finally have:

2 \sqrt [3] {3} - \sqrt [3] {18}

Answer:

2 \sqrt [3] {3} - \sqrt [3] {18}

5 0
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