Basic Math Examples

$A = {({(\frac{1}{8})}^{2} \cdot {(\frac{- 2}{5})}^{6} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 1

Apply the product rule to $\frac{1}{8}$ .

$A = {(\frac{1^{2}}{8^{2}} \cdot {(\frac{- 2}{5})}^{6} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 2

One to any power is one.

$A = {(\frac{1}{8^{2}} \cdot {(\frac{- 2}{5})}^{6} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 3

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

$A = {(\frac{1}{64} \cdot {(\frac{- 2}{5})}^{6} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 4

Move the negative in front of the fraction.

$A = {(\frac{1}{64} \cdot {(- \frac{2}{5})}^{6} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $- \frac{2}{5}$ .

$A = {(\frac{1}{64} \cdot ({(- 1)}^{6} {(\frac{2}{5})}^{6}) \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 5.2

Apply the product rule to $\frac{2}{5}$ .

$A = {(\frac{1}{64} \cdot ({(- 1)}^{6} \frac{2^{6}}{5^{6}}) \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 6

Simplify the expression.

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Step 6.1

Raise $- 1$ to the power of $6$ .

$A = {(\frac{1}{64} \cdot (1 \frac{2^{6}}{5^{6}}) \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 6.2

Multiply $\frac{2^{6}}{5^{6}}$ by $1$ .

$A = {(\frac{1}{64} \cdot \frac{2^{6}}{5^{6}} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 7

Combine.

$A = {(\frac{1 \cdot 2^{6}}{64 \cdot 5^{6}} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $2^{6}$ by $1$ .

$A = {(\frac{2^{6}}{64 \cdot 5^{6}} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 8.2

Raise $5$ to the power of $6$ .

$A = {(\frac{2^{6}}{64 \cdot 15625} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 8.3

Raise $2$ to the power of $6$ .

$A = {(\frac{64}{64 \cdot 15625} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 8.4

Multiply $64$ by $15625$ .

$A = {(\frac{64}{1000000} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 9

Cancel the common factor of $64$ and $1000000$ .

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Step 9.1

Factor $64$ out of $64$ .

$A = {(\frac{64 (1)}{1000000} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $64$ out of $1000000$ .

$A = {(\frac{64 \cdot 1}{64 \cdot 15625} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 9.2.2

Cancel the common factor.

$A = {(\frac{64 \cdot 1}{64 \cdot 15625} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 9.2.3

Rewrite the expression.

$A = {(\frac{1}{15625} \cdot {(- \frac{5}{2})}^{4})}^{2}$

Step 10

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 10.1

Apply the product rule to $- \frac{5}{2}$ .

$A = {(\frac{1}{15625} \cdot ({(- 1)}^{4} {(\frac{5}{2})}^{4}))}^{2}$

Step 10.2

Apply the product rule to $\frac{5}{2}$ .

$A = {(\frac{1}{15625} \cdot ({(- 1)}^{4} \frac{5^{4}}{2^{4}}))}^{2}$

Step 11

Simplify the expression.

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Step 11.1

Raise $- 1$ to the power of $4$ .

$A = {(\frac{1}{15625} \cdot (1 \frac{5^{4}}{2^{4}}))}^{2}$

Step 11.2

Multiply $\frac{5^{4}}{2^{4}}$ by $1$ .

$A = {(\frac{1}{15625} \cdot \frac{5^{4}}{2^{4}})}^{2}$

Step 12

Combine.

$A = {(\frac{1 \cdot 5^{4}}{15625 \cdot 2^{4}})}^{2}$

Step 13

Simplify the expression.

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Step 13.1

Multiply $5^{4}$ by $1$ .

$A = {(\frac{5^{4}}{15625 \cdot 2^{4}})}^{2}$

Step 13.2

Raise $2$ to the power of $4$ .

$A = {(\frac{5^{4}}{15625 \cdot 16})}^{2}$

Step 13.3

Raise $5$ to the power of $4$ .

$A = {(\frac{625}{15625 \cdot 16})}^{2}$

Step 13.4

Multiply $15625$ by $16$ .

$A = {(\frac{625}{250000})}^{2}$

Step 14

Cancel the common factor of $625$ and $250000$ .

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Step 14.1

Factor $625$ out of $625$ .

$A = {(\frac{625 (1)}{250000})}^{2}$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Factor $625$ out of $250000$ .

$A = {(\frac{625 \cdot 1}{625 \cdot 400})}^{2}$

Step 14.2.2

Cancel the common factor.

$A = {(\frac{625 \cdot 1}{625 \cdot 400})}^{2}$

Step 14.2.3

Rewrite the expression.

$A = {(\frac{1}{400})}^{2}$

Step 15

Simplify the expression.

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Step 15.1

Apply the product rule to $\frac{1}{400}$ .

$A = \frac{1^{2}}{400^{2}}$

Step 15.2

One to any power is one.

$A = \frac{1}{400^{2}}$

Step 15.3

Raise $400$ to the power of $2$ .

$A = \frac{1}{160000}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$A = \frac{1}{160000}$

Decimal Form:

$A = 6.25 \cdot 10^{- 6}$