Algebra Examples

$A = {(\frac{1}{4})}^{- {(\frac{1}{4})}^{- 1}} + {(\frac{1}{5})}^{- {(\frac{1}{2})}^{- 1}} + {(- 1)}^{3456}$

Step 1

Simplify each term.

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Step 1.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$A = {(\frac{1}{4})}^{- 1 \cdot 4} + {(\frac{1}{5})}^{- {(\frac{1}{2})}^{- 1}} + {(- 1)}^{3456}$

Step 1.2

Multiply $- 1$ by $4$ .

$A = {(\frac{1}{4})}^{- 4} + {(\frac{1}{5})}^{- {(\frac{1}{2})}^{- 1}} + {(- 1)}^{3456}$

Step 1.3

Change the sign of the exponent by rewriting the base as its reciprocal.

$A = 4^{4} + {(\frac{1}{5})}^{- {(\frac{1}{2})}^{- 1}} + {(- 1)}^{3456}$

Step 1.4

Raise $4$ to the power of $4$ .

$A = 256 + {(\frac{1}{5})}^{- {(\frac{1}{2})}^{- 1}} + {(- 1)}^{3456}$

Step 1.5

Change the sign of the exponent by rewriting the base as its reciprocal.

$A = 256 + {(\frac{1}{5})}^{- 1 \cdot 2} + {(- 1)}^{3456}$

Step 1.6

Multiply $- 1$ by $2$ .

$A = 256 + {(\frac{1}{5})}^{- 2} + {(- 1)}^{3456}$

Step 1.7

Change the sign of the exponent by rewriting the base as its reciprocal.

$A = 256 + 5^{2} + {(- 1)}^{3456}$

Step 1.8

Raise $5$ to the power of $2$ .

$A = 256 + 25 + {(- 1)}^{3456}$

Step 1.9

Raise $- 1$ to the power of $3456$ .

$A = 256 + 25 + 1$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $256$ and $25$ .

$A = 281 + 1$

Step 2.2

Add $281$ and $1$ .

$A = 282$