Basic Math Examples

${(2^{8} \cdot 5^{- 5} \cdot 19^{0})}^{- 2}$

Step 1

Raise $2$ to the power of $8$ .

${(256 \cdot 5^{- 5} \cdot 19^{0})}^{- 2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(256 \cdot \frac{1}{5^{5}} \cdot 19^{0})}^{- 2}$

Step 3

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

${(256 \cdot \frac{1}{3125} \cdot 19^{0})}^{- 2}$

Step 4

Combine $256$ and $\frac{1}{3125}$ .

${(\frac{256}{3125} \cdot 19^{0})}^{- 2}$

Step 5

Simplify the expression.

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Step 5.1

Anything raised to $0$ is $1$ .

${(\frac{256}{3125} \cdot 1)}^{- 2}$

Step 5.2

Multiply $\frac{256}{3125}$ by $1$ .

${(\frac{256}{3125})}^{- 2}$

Step 6

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

${(\frac{3125}{256})}^{2}$

Step 7

Apply the product rule to $\frac{3125}{256}$ .

$\frac{3125^{2}}{256^{2}}$

Step 8

Raise $3125$ to the power of $2$ .

$\frac{9765625}{256^{2}}$

Step 9

Raise $256$ to the power of $2$ .

$\frac{9765625}{65536}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{9765625}{65536}$

Decimal Form:

$149.01161193 \dots$

Mixed Number Form:

$149 \frac{761}{65536}$