Basic Math Examples

$\frac{15}{8} \cdot \frac{5}{4^{2}}$

Step 1

Combine fractions.

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Step 1.1

Combine.

$\frac{15 \cdot 5}{8 \cdot 4^{2}}$

Step 1.2

Multiply $15$ by $5$ .

$\frac{75}{8 \cdot 4^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $8$ as $2^{3}$ .

$\frac{75}{2^{3} \cdot 4^{2}}$

Step 2.2

Rewrite $4$ as $2^{2}$ .

$\frac{75}{2^{3} \cdot {(2^{2})}^{2}}$

Step 2.3

Multiply the exponents in ${(2^{2})}^{2}$ .

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Step 2.3.1

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

$\frac{75}{2^{3} \cdot 2^{2 \cdot 2}}$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{75}{2^{3} \cdot 2^{4}}$

Step 2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{75}{2^{3 + 4}}$

Step 2.5

Add $3$ and $4$ .

$\frac{75}{2^{7}}$

Step 3

Raise $2$ to the power of $7$ .

$\frac{75}{128}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{75}{128}$

Decimal Form:

$0.5859375$