Basic Math Examples

$\frac{{(21)}^{3}}{{(15)}^{2}} \cdot \frac{{(35)}^{5}}{{(14)}^{10}} \cdot \frac{{(80)}^{3}}{{(30)}^{2}}$

Step 1

Simplify terms.

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Step 1.1

Raise $80$ to the power of $3$ .

$\frac{{(21)}^{3}}{{(15)}^{2}} \cdot \frac{{(35)}^{5}}{{(14)}^{10}} \cdot \frac{512000}{{(30)}^{2}}$

Step 1.2

Raise $30$ to the power of $2$ .

$\frac{{(21)}^{3}}{{(15)}^{2}} \cdot \frac{{(35)}^{5}}{{(14)}^{10}} \cdot \frac{512000}{900}$

Step 1.3

Combine.

$\frac{{(21)}^{3} {(35)}^{5}}{{(15)}^{2} {(14)}^{10}} \cdot \frac{512000}{900}$

Step 1.4

Combine.

$\frac{{(21)}^{3} {(35)}^{5} \cdot 512000}{{(15)}^{2} {(14)}^{10} \cdot 900}$

Step 1.5

Cancel the common factor of $512000$ and $900$ .

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Step 1.5.1

Factor $100$ out of ${(21)}^{3} {(35)}^{5} \cdot 512000$ .

$\frac{100 ({(21)}^{3} {(35)}^{5} \cdot 5120)}{{(15)}^{2} {(14)}^{10} \cdot 900}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $100$ out of ${(15)}^{2} {(14)}^{10} \cdot 900$ .

$\frac{100 ({(21)}^{3} {(35)}^{5} \cdot 5120)}{100 ({(15)}^{2} {(14)}^{10} \cdot 9)}$

Step 1.5.2.2

Cancel the common factor.

$\frac{100 ({(21)}^{3} {(35)}^{5} \cdot 5120)}{100 ({(15)}^{2} {(14)}^{10} \cdot 9)}$

Step 1.5.2.3

Rewrite the expression.

$\frac{{(21)}^{3} {(35)}^{5} \cdot 5120}{{(15)}^{2} {(14)}^{10} \cdot 9}$

Step 2

Simplify the numerator.

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Step 2.1

Raise $21$ to the power of $3$ .

$\frac{9261 \cdot 35^{5} \cdot 5120}{15^{2} \cdot 14^{10} \cdot 9}$

Step 2.2

Raise $35$ to the power of $5$ .

$\frac{9261 \cdot 52521875 \cdot 5120}{15^{2} \cdot 14^{10} \cdot 9}$

Step 2.3

Combine exponents.

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Step 2.3.1

Multiply $9261$ by $52521875$ .

$\frac{486405084375 \cdot 5120}{15^{2} \cdot 14^{10} \cdot 9}$

Step 2.3.2

Multiply $486405084375$ by $5120$ .

$\frac{2490394032000000}{15^{2} \cdot 14^{10} \cdot 9}$

Step 3

Simplify the denominator.

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Step 3.1

Raise $15$ to the power of $2$ .

$\frac{2490394032000000}{225 \cdot 14^{10} \cdot 9}$

Step 3.2

Raise $14$ to the power of $10$ .

$\frac{2490394032000000}{225 \cdot 289254654976 \cdot 9}$

Step 3.3

Combine exponents.

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Step 3.3.1

Multiply $225$ by $289254654976$ .

$\frac{2490394032000000}{65082297369600 \cdot 9}$

Step 3.3.2

Multiply $65082297369600$ by $9$ .

$\frac{2490394032000000}{585740676326400}$

Step 4

Cancel the common factor of $2490394032000000$ and $585740676326400$ .

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Step 4.1

Factor $3984630451200$ out of $2490394032000000$ .

$\frac{3984630451200 (625)}{585740676326400}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3984630451200$ out of $585740676326400$ .

$\frac{3984630451200 \cdot 625}{3984630451200 \cdot 147}$

Step 4.2.2

Cancel the common factor.

$\frac{3984630451200 \cdot 625}{3984630451200 \cdot 147}$

Step 4.2.3

Rewrite the expression.

$\frac{625}{147}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{625}{147}$

Decimal Form:

$4.25170068 \dots$

Mixed Number Form:

$4 \frac{37}{147}$