What is {[(5/4-3)^{-2}]^{-2}}^{-1} ?

The solution to {[(5/4-3)^{-2}]^{-2}}^{-1} is 256/2401

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simplify {[(5/4-3)^{-2}]^{-2}}^{-1}

simplify

⎩ ⎨ ⎧ [(\frac{5}{4} - 3)^{- 2}]^{- 2} ⎭ ⎬ ⎫^{- 1}

\frac{256}{2401}

Decimal Notation

0.10662 \dots

Solution steps

⎩ ⎨ ⎧ [(\frac{5}{4} - 3)^{- 2}]^{- 2} ⎭ ⎬ ⎫^{- 1}

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

= {(\frac{5}{4} - 3)^{4}}^{- 1}

(\frac{5}{4} - 3)^{4} = \frac{7 ^{4}}{4 ^{4}}

= (\frac{7 ^{4}}{4 ^{4}})^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{\frac{7 ^{4}}{4 ^{4}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{4 ^{4}}{7 ^{4}}

4^{4} = 256

= \frac{256}{7 ^{4}}

7^{4} = 2401

= \frac{256}{2401}

0^{2} e^{- 0}

\frac{( ( \frac{4}{7} ) ^{6} )}{( ( \frac{4}{7} ) ^{- 6} )}

e^{- a x} \cdot e^{- b x}

80000 (1 + \frac{0.85}{12})^{- 60}

What is {[(5/4-3)^{-2}]^{-2}}^{-1} ?
The solution to {[(5/4-3)^{-2}]^{-2}}^{-1} is 256/2401