Algebra Examples

$\frac{(3^{7} \cdot 4^{7}) {(2 \cdot 5)}^{- 3} (5^{2})}{12^{7} \cdot 5^{- 1} \cdot 2^{- 4}}$

Step 1

Move ${(2 \cdot 5)}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3^{7} \cdot 4^{7} \cdot 5^{2}}{12^{7} \cdot 5^{- 1} \cdot 2^{- 4} {(2 \cdot 5)}^{3}}$

Step 2

Move $5^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3^{7} \cdot 4^{7} \cdot 5^{2} \cdot 5}{12^{7} \cdot 2^{- 4} {(2 \cdot 5)}^{3}}$

Step 3

Move $2^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3^{7} \cdot 4^{7} \cdot 5^{2} \cdot 5 \cdot 2^{4}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 4

Multiply $5^{2}$ by $5$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $5$ .

$\frac{3^{7} \cdot 4^{7} \cdot (5 \cdot 5^{2}) \cdot 2^{4}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 4.2

Multiply $5$ by $5^{2}$ .

Tap for more steps...

Step 4.2.1

Raise $5$ to the power of $1$ .

$\frac{3^{7} \cdot 4^{7} \cdot (5^{1} \cdot 5^{2}) \cdot 2^{4}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 4.2.2

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

$\frac{3^{7} \cdot 4^{7} \cdot 5^{1 + 2} \cdot 2^{4}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 4.3

Add $1$ and $2$ .

$\frac{3^{7} \cdot 4^{7} \cdot 5^{3} \cdot 2^{4}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

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

$\frac{3^{7} \cdot (2^{4} \cdot {(2^{2})}^{7}) \cdot 5^{3}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 5.2

Multiply the exponents in ${(2^{2})}^{7}$ .

Tap for more steps...

Step 5.2.1

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

$\frac{3^{7} \cdot (2^{4} \cdot 2^{2 \cdot 7}) \cdot 5^{3}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 5.2.2

Multiply $2$ by $7$ .

$\frac{3^{7} \cdot (2^{4} \cdot 2^{14}) \cdot 5^{3}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 5.3

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

$\frac{3^{7} \cdot 2^{4 + 14} \cdot 5^{3}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 5.4

Add $4$ and $14$ .

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{12^{7} {(2 \cdot 5)}^{3}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

Apply the product rule to $2 \cdot 5$ .

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{12^{7} \cdot 2^{3} \cdot 5^{3}}$

Step 6.2

Raise $12$ to the power of $7$ .

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{35831808 \cdot 2^{3} \cdot 5^{3}}$

Step 6.3

Raise $2$ to the power of $3$ .

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{35831808 \cdot 8 \cdot 5^{3}}$

Step 6.4

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

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{35831808 \cdot 8 \cdot 125}$

Step 6.5

Combine exponents.

Tap for more steps...

Step 6.5.1

Multiply $35831808$ by $8$ .

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{286654464 \cdot 125}$

Step 6.5.2

Multiply $286654464$ by $125$ .

$\frac{3^{7} \cdot 2^{18} \cdot 5^{3}}{35831808000}$

Step 7

Simplify the numerator.

Tap for more steps...

Step 7.1

Raise $3$ to the power of $7$ .

$\frac{2187 \cdot 2^{18} \cdot 5^{3}}{35831808000}$

Step 7.2

Raise $2$ to the power of $18$ .

$\frac{2187 \cdot 262144 \cdot 5^{3}}{35831808000}$

Step 7.3

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

$\frac{2187 \cdot 262144 \cdot 125}{35831808000}$

Step 7.4

Combine exponents.

Tap for more steps...

Step 7.4.1

Multiply $2187$ by $262144$ .

$\frac{573308928 \cdot 125}{35831808000}$

Step 7.4.2

Multiply $573308928$ by $125$ .

$\frac{71663616000}{35831808000}$

Step 8

Divide $71663616000$ by $35831808000$ .

$2$