Basic Math Examples

${(\frac{4}{5})}^{2} \cdot {({(\frac{5}{4})}^{3})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{4}{5}$ .

$\frac{4^{2}}{5^{2}} \cdot {({(\frac{5}{4})}^{3})}^{2}$

Step 1.2

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

$\frac{16}{5^{2}} \cdot {({(\frac{5}{4})}^{3})}^{2}$

Step 1.3

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

$\frac{16}{25} \cdot {({(\frac{5}{4})}^{3})}^{2}$

Step 1.4

Multiply the exponents in ${({(\frac{5}{4})}^{3})}^{2}$ .

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Step 1.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{16}{25} \cdot {(\frac{5}{4})}^{3 \cdot 2}$

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{16}{25} \cdot {(\frac{5}{4})}^{6}$

Step 1.5

Apply the product rule to $\frac{5}{4}$ .

$\frac{16}{25} \cdot \frac{5^{6}}{4^{6}}$

Step 2

Combine.

$\frac{16 \cdot 5^{6}}{25 \cdot 4^{6}}$

Step 3

Simplify the expression.

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Step 3.1

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

$\frac{16 \cdot 15625}{25 \cdot 4^{6}}$

Step 3.2

Raise $4$ to the power of $6$ .

$\frac{16 \cdot 15625}{25 \cdot 4096}$

Step 3.3

Multiply $16$ by $15625$ .

$\frac{250000}{25 \cdot 4096}$

Step 3.4

Multiply $25$ by $4096$ .

$\frac{250000}{102400}$

Step 4

Cancel the common factor of $250000$ and $102400$ .

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Step 4.1

Factor $400$ out of $250000$ .

$\frac{400 (625)}{102400}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $400$ out of $102400$ .

$\frac{400 \cdot 625}{400 \cdot 256}$

Step 4.2.2

Cancel the common factor.

$\frac{400 \cdot 625}{400 \cdot 256}$

Step 4.2.3

Rewrite the expression.

$\frac{625}{256}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{625}{256}$

Decimal Form:

$2.44140625$

Mixed Number Form:

$2 \frac{113}{256}$