Basic Math Examples

${(\frac{2^{2} \cdot 5^{3}}{15})}^{4}$

Step 1

Simplify the numerator.

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Step 1.1

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

${(\frac{4 \cdot 5^{3}}{15})}^{4}$

Step 1.2

Raise $5$ to the power of $3$ .

${(\frac{4 \cdot 125}{15})}^{4}$

${(\frac{4 \cdot 125}{15})}^{4}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Multiply $4$ by $125$ .

${(\frac{500}{15})}^{4}$

Step 2.2

Cancel the common factor of $500$ and $15$ .

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Step 2.2.1

Factor $5$ out of $500$ .

${(\frac{5 (100)}{15})}^{4}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $5$ out of $15$ .

${(\frac{5 \cdot 100}{5 \cdot 3})}^{4}$

Step 2.2.2.2

Cancel the common factor.

${(\frac{5 \cdot 100}{5 \cdot 3})}^{4}$

Step 2.2.2.3

Rewrite the expression.

${(\frac{100}{3})}^{4}$

${(\frac{100}{3})}^{4}$

${(\frac{100}{3})}^{4}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Apply the product rule to $\frac{100}{3}$ .

$\frac{100^{4}}{3^{4}}$

Step 2.3.2

Raise $100$ to the power of $4$ .

$\frac{100000000}{3^{4}}$

Step 2.3.3

Raise $3$ to the power of $4$ .

$\frac{100000000}{81}$

$\frac{100000000}{81}$

$\frac{100000000}{81}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{100000000}{81}$

Decimal Form:

$1234567.90123457$

Mixed Number Form:

$1234567 \frac{73}{81}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$