Basic Math Examples

${(2^{8} \cdot 5^{- 5} \cdot 19^{0})}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 1

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

${(256 \cdot 5^{- 5} \cdot 19^{0})}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 2

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

${(256 \cdot \frac{1}{5^{5}} \cdot 19^{0})}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 3

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

${(256 \cdot \frac{1}{3125} \cdot 19^{0})}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 4

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

${(\frac{256}{3125} \cdot 19^{0})}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 5

Simplify the expression.

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Step 5.1

Anything raised to $0$ is $1$ .

${(\frac{256}{3125} \cdot 1)}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 5.2

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

${(\frac{256}{3125})}^{- 2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 6

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

${(\frac{3125}{256})}^{2} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 7

Simplify the expression.

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Step 7.1

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

$\frac{3125^{2}}{256^{2}} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 7.2

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

$\frac{9765625}{256^{2}} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 7.3

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

$\frac{9765625}{65536} \cdot {(\frac{5^{- 5}}{2^{3}})}^{4} \cdot 2^{28}$

Step 7.4

Move $5^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{9765625}{65536} \cdot {(\frac{1}{2^{3} \cdot 5^{5}})}^{4} \cdot 2^{28}$

Step 8

Simplify the denominator.

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Step 8.1

Raise $2$ to the power of $3$ .

$\frac{9765625}{65536} \cdot {(\frac{1}{8 \cdot 5^{5}})}^{4} \cdot 2^{28}$

Step 8.2

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

$\frac{9765625}{65536} \cdot {(\frac{1}{8 \cdot 3125})}^{4} \cdot 2^{28}$

Step 9

Simplify terms.

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Step 9.1

Multiply $8$ by $3125$ .

$\frac{9765625}{65536} \cdot {(\frac{1}{25000})}^{4} \cdot 2^{28}$

Step 9.2

Apply the product rule to $\frac{1}{25000}$ .

$\frac{9765625}{65536} \cdot \frac{1^{4}}{25000^{4}} \cdot 2^{28}$

Step 9.3

Combine.

$\frac{9765625 \cdot 1^{4}}{65536 \cdot 25000^{4}} \cdot 2^{28}$

Step 9.4

Simplify the expression.

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Step 9.4.1

One to any power is one.

$\frac{9765625 \cdot 1}{65536 \cdot 25000^{4}} \cdot 2^{28}$

Step 9.4.2

Raise $25000$ to the power of $4$ .

$\frac{9765625 \cdot 1}{65536 \cdot 390625000000000000} \cdot 2^{28}$

Step 9.4.3

Multiply $9765625$ by $1$ .

$\frac{9765625}{65536 \cdot 390625000000000000} \cdot 2^{28}$

Step 9.4.4

Multiply $65536$ by $390625000000000000$ .

$\frac{9765625}{25600000000000000000000} \cdot 2^{28}$

Step 9.5

Cancel the common factor of $9765625$ and $25600000000000000000000$ .

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Step 9.5.1

Factor $9765625$ out of $9765625$ .

$\frac{9765625 (1)}{25600000000000000000000} \cdot 2^{28}$

Step 9.5.2

Cancel the common factors.

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Step 9.5.2.1

Factor $9765625$ out of $25600000000000000000000$ .

$\frac{9765625 \cdot 1}{9765625 \cdot 2621440000000000} \cdot 2^{28}$

Step 9.5.2.2

Cancel the common factor.

$\frac{9765625 \cdot 1}{9765625 \cdot 2621440000000000} \cdot 2^{28}$

Step 9.5.2.3

Rewrite the expression.

$\frac{1}{2621440000000000} \cdot 2^{28}$

Step 9.6

Raise $2$ to the power of $28$ .

$\frac{1}{2621440000000000} \cdot 268435456$

Step 9.7

Cancel the common factor of $268435456$ .

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Step 9.7.1

Factor $268435456$ out of $2621440000000000$ .

$\frac{1}{268435456 (9765625)} \cdot 268435456$

Step 9.7.2

Cancel the common factor.

$\frac{1}{268435456 \cdot 9765625} \cdot 268435456$

Step 9.7.3

Rewrite the expression.

$\frac{1}{9765625}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9765625}$

Decimal Form:

$1.024 \cdot 10^{- 7}$