What is ([ 9/4 (9/4)^5]^2)/([(9/4)^2 9/4 ]^2) ?

The solution to ([ 9/4 (9/4)^5]^2)/([(9/4)^2 9/4 ]^2) is 531441/4096

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simplify ([ 9/4 (9/4)^5]^2)/([(9/4)^2 9/4 ]^2)

simplify

\frac{[ \frac{9}{4} ( \frac{9}{4} ) ^{5} ] ^{2}}{[ ( \frac{9}{4} ) ^{2} \frac{9}{4} ] ^{2}}

\frac{531441}{4096}

Decimal Notation

129.74633 \dots

Solution steps

\frac{( \frac{9}{4} ( \frac{9}{4} ) ^{5} ) ^{2}}{( ( \frac{9}{4} ) ^{2} \frac{9}{4} ) ^{2}}

Apply the commutative law:

(\frac{9}{4})^{2} \frac{9}{4} = \frac{9}{4} (\frac{9}{4})^{2}

= \frac{( \frac{9}{4} ( \frac{9}{4} ) ^{5} ) ^{2}}{( \frac{9}{4} ( \frac{9}{4} ) ^{2} ) ^{2}}

(\frac{9}{4} (\frac{9}{4})^{5})^{2} = (\frac{9}{4})^{2} \frac{9 ^{10}}{4 ^{10}}

= \frac{( \frac{9}{4} ) ^{2} \frac{9 ^{10}}{4 ^{10}}}{( \frac{9}{4} ( \frac{9}{4} ) ^{2} ) ^{2}}

(\frac{9}{4} (\frac{9}{4})^{2})^{2} = (\frac{9}{4})^{2} \frac{6561}{256}

= \frac{( \frac{9}{4} ) ^{2} \frac{9 ^{10}}{4 ^{10}}}{( \frac{9}{4} ) ^{2} \frac{6561}{256}}

Cancel the common factor:

(\frac{9}{4})^{2}

= \frac{\frac{9 ^{10}}{4 ^{10}}}{\frac{6561}{256}}

\frac{\frac{9 ^{10}}{4 ^{10}}}{\frac{6561}{256}} = \frac{531441}{4096}

= \frac{531441}{4096}

e^{- 1000.4}

e^{- 6} \cdot 6^{4}

- 0.37 (6. 2^{- 2})

(7 \cdot 2) (5 \cdot 2)

(2.5 \cdot 1 0^{7}) \cdot (3 \cdot 1 0^{2})

What is ([ 9/4 (9/4)^5]^2)/([(9/4)^2 9/4 ]^2) ?
The solution to ([ 9/4 (9/4)^5]^2)/([(9/4)^2 9/4 ]^2) is 531441/4096