What is (2/3)^5(2/3)^{-3}(2/3)^4(2/3)^5 ?

The solution to (2/3)^5(2/3)^{-3}(2/3)^4(2/3)^5 is 2048/177147

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simplify (2/3)^5(2/3)^{-3}(2/3)^4(2/3)^5

simplify

(\frac{2}{3})^{5} (\frac{2}{3})^{- 3} (\frac{2}{3})^{4} (\frac{2}{3})^{5}

\frac{2048}{177147}

Decimal Notation

0.01156 \dots

Solution steps

(\frac{2}{3})^{5} (\frac{2}{3})^{- 3} (\frac{2}{3})^{4} (\frac{2}{3})^{5}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

(\frac{2}{3})^{5} (\frac{2}{3})^{- 3} (\frac{2}{3})^{4} (\frac{2}{3})^{5} = (\frac{2}{3})^{5 - 3 + 4 + 5}

= (\frac{2}{3})^{5 - 3 + 4 + 5}

Add/Subtract the numbers:

5 - 3 + 4 + 5 = 11

= (\frac{2}{3})^{11}

Apply exponent rule:

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

= \frac{2 ^{11}}{3 ^{11}}

2^{11} = 2048

= \frac{2048}{3 ^{11}}

3^{11} = 177147

= \frac{2048}{177147}

3 m - 2 n - 2 n x^{4} + 3 m x^{4}

\frac{1}{2} - \frac{5}{3}

3 m^{2} (m - 2 n) - 4 mn (m - 2 n) - 4 n^{2} (m - 2 n)

3 t^{2} + t - 2

x^{2} - 2 x + 3 \geq 0

What is (2/3)^5(2/3)^{-3}(2/3)^4(2/3)^5 ?
The solution to (2/3)^5(2/3)^{-3}(2/3)^4(2/3)^5 is 2048/177147