Basic Math Examples

$35^{4} \cdot 14^{- 3} \cdot 25^{- 2} \cdot 8^{2}$

Step 1

Raise $35$ to the power of $4$ .

$1500625 \cdot 14^{- 3} \cdot 25^{- 2} \cdot 8^{2}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$1500625 \cdot \frac{1}{14^{3}} \cdot 25^{- 2} \cdot 8^{2}$

Step 3

Raise $14$ to the power of $3$ .

$1500625 \cdot \frac{1}{2744} \cdot 25^{- 2} \cdot 8^{2}$

Step 4

Cancel the common factor of $343$ .

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Step 4.1

Factor $343$ out of $1500625$ .

$343 (4375) \cdot \frac{1}{2744} \cdot 25^{- 2} \cdot 8^{2}$

Step 4.2

Factor $343$ out of $2744$ .

$343 \cdot 4375 \cdot \frac{1}{343 \cdot 8} \cdot 25^{- 2} \cdot 8^{2}$

Step 4.3

Cancel the common factor.

$343 \cdot 4375 \cdot \frac{1}{343 \cdot 8} \cdot 25^{- 2} \cdot 8^{2}$

Step 4.4

Rewrite the expression.

$4375 \cdot \frac{1}{8} \cdot 25^{- 2} \cdot 8^{2}$

Step 5

Combine $4375$ and $\frac{1}{8}$ .

$\frac{4375}{8} \cdot 25^{- 2} \cdot 8^{2}$

Step 6

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4375}{8} \cdot \frac{1}{25^{2}} \cdot 8^{2}$

Step 7

Combine.

$\frac{4375 \cdot 1}{8 \cdot 25^{2}} \cdot 8^{2}$

Step 8

Simplify the expression.

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Step 8.1

Multiply $4375$ by $1$ .

$\frac{4375}{8 \cdot 25^{2}} \cdot 8^{2}$

Step 8.2

Raise $25$ to the power of $2$ .

$\frac{4375}{8 \cdot 625} \cdot 8^{2}$

Step 8.3

Multiply $8$ by $625$ .

$\frac{4375}{5000} \cdot 8^{2}$

Step 9

Cancel the common factor of $4375$ and $5000$ .

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Step 9.1

Factor $625$ out of $4375$ .

$\frac{625 (7)}{5000} \cdot 8^{2}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $625$ out of $5000$ .

$\frac{625 \cdot 7}{625 \cdot 8} \cdot 8^{2}$

Step 9.2.2

Cancel the common factor.

$\frac{625 \cdot 7}{625 \cdot 8} \cdot 8^{2}$

Step 9.2.3

Rewrite the expression.

$\frac{7}{8} \cdot 8^{2}$

Step 10

Cancel the common factor of $8$ .

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Step 10.1

Factor $8$ out of $8^{2}$ .

$\frac{7}{8} \cdot (8 \cdot 8)$

Step 10.2

Cancel the common factor.

$\frac{7}{8} \cdot (8 \cdot 8)$

Step 10.3

Rewrite the expression.

$7 \cdot 8$

Step 11

Multiply $7$ by $8$ .

$56$