Basic Math Examples

$\frac{(3 t^{2} z^{- 4}) \cdot (34 z^{- 2})}{2 t^{- 2} z^{4}} \div \frac{{(2 t z)}^{5}}{t^{4} z^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{(3 t^{2} z^{- 4}) \cdot (34 z^{- 2})}{2 t^{- 2} z^{4}} \cdot \frac{t^{4} z^{3}}{{(2 t z)}^{5}}$

Step 2

Combine.

$\frac{(3 t^{2} z^{- 4}) \cdot (34 z^{- 2}) (t^{4} z^{3})}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 3

Multiply $z^{- 4}$ by $z^{- 2}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $z^{- 2}$ .

$\frac{3 t^{2} (z^{- 2} z^{- 4}) \cdot 34 (t^{4} z^{3})}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 3.2

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

$\frac{3 t^{2} z^{- 2 - 4} \cdot 34 (t^{4} z^{3})}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 3.3

Subtract $4$ from $- 2$ .

$\frac{3 t^{2} z^{- 6} \cdot 34 (t^{4} z^{3})}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 4

Multiply $t^{2}$ by $t^{4}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $t^{4}$ .

$\frac{3 (t^{4} t^{2}) z^{- 6} \cdot 34 z^{3}}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 4.2

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

$\frac{3 t^{4 + 2} z^{- 6} \cdot 34 z^{3}}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 4.3

Add $4$ and $2$ .

$\frac{3 t^{6} z^{- 6} \cdot 34 z^{3}}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 5

Multiply $z^{- 6}$ by $z^{3}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $z^{3}$ .

$\frac{3 t^{6} (z^{3} z^{- 6}) \cdot 34}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 5.2

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

$\frac{3 t^{6} z^{3 - 6} \cdot 34}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 5.3

Subtract $6$ from $3$ .

$\frac{3 t^{6} z^{- 3} \cdot 34}{2 t^{- 2} z^{4} {(2 t z)}^{5}}$

Step 6

Move $z^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3 t^{6} \cdot 34}{2 t^{- 2} z^{4} {(2 t z)}^{5} z^{3}}$

Step 7

Multiply $z^{4}$ by $z^{3}$ by adding the exponents.

Tap for more steps...

Step 7.1

Move $z^{3}$ .

$\frac{3 t^{6} \cdot 34}{2 t^{- 2} (z^{3} z^{4}) {(2 t z)}^{5}}$

Step 7.2

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

$\frac{3 t^{6} \cdot 34}{2 t^{- 2} z^{3 + 4} {(2 t z)}^{5}}$

Step 7.3

Add $3$ and $4$ .

$\frac{3 t^{6} \cdot 34}{2 t^{- 2} z^{7} {(2 t z)}^{5}}$

Step 8

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

$\frac{3 t^{6} \cdot 34 t^{2}}{2 z^{7} {(2 t z)}^{5}}$

Step 9

Multiply $t^{6}$ by $t^{2}$ by adding the exponents.

Tap for more steps...

Step 9.1

Move $t^{2}$ .

$\frac{3 (t^{2} t^{6}) \cdot 34}{2 z^{7} {(2 t z)}^{5}}$

Step 9.2

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

$\frac{3 t^{2 + 6} \cdot 34}{2 z^{7} {(2 t z)}^{5}}$

Step 9.3

Add $2$ and $6$ .

$\frac{3 t^{8} \cdot 34}{2 z^{7} {(2 t z)}^{5}}$

Step 10

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 10.1

Cancel the common factor of $34$ and $2$ .

Tap for more steps...

Step 10.1.1

Factor $2$ out of $3 t^{8} \cdot 34$ .

$\frac{2 (3 t^{8} \cdot 17)}{2 z^{7} {(2 t z)}^{5}}$

Step 10.1.2

Cancel the common factors.

Tap for more steps...

Step 10.1.2.1

Factor $2$ out of $2 z^{7} {(2 t z)}^{5}$ .

$\frac{2 (3 t^{8} \cdot 17)}{2 (z^{7} {(2 t z)}^{5})}$

Step 10.1.2.2

Cancel the common factor.

$\frac{2 (3 t^{8} \cdot 17)}{2 (z^{7} {(2 t z)}^{5})}$

Step 10.1.2.3

Rewrite the expression.

$\frac{3 t^{8} \cdot 17}{z^{7} {(2 t z)}^{5}}$

Step 10.2

Multiply $17$ by $3$ .

$\frac{51 t^{8}}{z^{7} {(2 t z)}^{5}}$

Step 11

Simplify the denominator.

Tap for more steps...

Step 11.1

Apply the product rule to $2 t z$ .

$\frac{51 t^{8}}{z^{7} {(2 t)}^{5} z^{5}}$

Step 11.2

Multiply $z^{7}$ by $z^{5}$ by adding the exponents.

Tap for more steps...

Step 11.2.1

Move $z^{5}$ .

$\frac{51 t^{8}}{z^{5} z^{7} {(2 t)}^{5}}$

Step 11.2.2

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

$\frac{51 t^{8}}{z^{5 + 7} {(2 t)}^{5}}$

Step 11.2.3

Add $5$ and $7$ .

$\frac{51 t^{8}}{z^{12} {(2 t)}^{5}}$

Step 11.3

Apply the product rule to $2 t$ .

$\frac{51 t^{8}}{z^{12} (2^{5} t^{5})}$

Step 11.4

Raise $2$ to the power of $5$ .

$\frac{51 t^{8}}{z^{12} \cdot 32 t^{5}}$

Step 12

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 12.1

Cancel the common factor of $t^{8}$ and $t^{5}$ .

Tap for more steps...

Step 12.1.1

Factor $t^{5}$ out of $51 t^{8}$ .

$\frac{t^{5} (51 t^{3})}{z^{12} \cdot 32 t^{5}}$

Step 12.1.2

Cancel the common factors.

Tap for more steps...

Step 12.1.2.1

Factor $t^{5}$ out of $z^{12} \cdot 32 t^{5}$ .

$\frac{t^{5} (51 t^{3})}{t^{5} (z^{12} \cdot 32)}$

Step 12.1.2.2

Cancel the common factor.

$\frac{t^{5} (51 t^{3})}{t^{5} (z^{12} \cdot 32)}$

Step 12.1.2.3

Rewrite the expression.

$\frac{51 t^{3}}{z^{12} \cdot 32}$

Step 12.2

Move $32$ to the left of $z^{12}$ .

$\frac{51 t^{3}}{32 z^{12}}$