What is (\sqrt[3]{4/6})^6*5/2 ?

The solution to (\sqrt[3]{4/6})^6*5/2 is 10/9

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simplify (\sqrt[3]{4/6})^6*5/2

simplify

\frac{10}{9}

Decimal Notation

1.11111 \dots

Solution steps

Rewrite

6

3 \cdot 2

Apply exponent rule:

a^{b c} = (a^{b})^{c}, a \geq 0

Apply exponent rule:

= (\frac{4}{6})^{2} \frac{5}{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{4}{6})^{2} = \frac{4 ^{2}}{6 ^{2}}

= \frac{4 ^{2}}{6 ^{2}} \cdot \frac{5}{2}

4^{2} = 16

= \frac{16}{6 ^{2}} \cdot \frac{5}{2}

6^{2} = 36

= \frac{16}{36} \cdot \frac{5}{2}

Cancel the common factor:

4

= \frac{4}{9} \cdot \frac{5}{2}

\frac{4}{9} \cdot \frac{5}{2} = \frac{10}{9}

= \frac{10}{9}

e^{2 x} \cdot e^{2 x}

x y

((θ) (4) (β^{3}) + β^{4}) ((θ) (4) (β^{3}) + β^{4})