Pre-Algebra Examples

$\frac{9 z^{5} x^{4}}{\frac{25}{\frac{45 x^{2} z^{7}}{35}}}$

Step 1

Cancel the common factor of $45$ and $35$ .

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Step 1.1

Factor $5$ out of $45 x^{2} z^{7}$ .

$\frac{9 z^{5} x^{4}}{\frac{25}{\frac{5 (9 x^{2} z^{7})}{35}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $35$ .

$\frac{9 z^{5} x^{4}}{\frac{25}{\frac{5 (9 x^{2} z^{7})}{5 (7)}}}$

Step 1.2.2

Cancel the common factor.

$\frac{9 z^{5} x^{4}}{\frac{25}{\frac{5 (9 x^{2} z^{7})}{5 \cdot 7}}}$

Step 1.2.3

Rewrite the expression.

$\frac{9 z^{5} x^{4}}{\frac{25}{\frac{9 x^{2} z^{7}}{7}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$9 z^{5} x^{4} \frac{\frac{9 x^{2} z^{7}}{7}}{25}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$9 z^{5} x^{4} (\frac{9 x^{2} z^{7}}{7} \cdot \frac{1}{25})$

Step 4

Combine.

$9 z^{5} x^{4} \frac{9 x^{2} z^{7} \cdot 1}{7 \cdot 25}$

Step 5

Multiply $9$ by $1$ .

$9 z^{5} x^{4} \frac{9 x^{2} z^{7}}{7 \cdot 25}$

Step 6

Multiply $7$ by $25$ .

$9 z^{5} x^{4} \frac{9 x^{2} z^{7}}{175}$

Step 7

Multiply $9 z^{5} x^{4} \frac{9 x^{2} z^{7}}{175}$ .

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Step 7.1

Combine $9$ and $\frac{9 x^{2} z^{7}}{175}$ .

$z^{5} x^{4} \frac{9 (9 x^{2} z^{7})}{175}$

Step 7.2

Multiply $9$ by $9$ .

$z^{5} x^{4} \frac{81 (x^{2} z^{7})}{175}$

Step 7.3

Combine $z^{5}$ and $\frac{81 (x^{2} z^{7})}{175}$ .

$x^{4} \frac{z^{5} (81 (x^{2} z^{7}))}{175}$

Step 7.4

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

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Step 7.4.1

Move $z^{7}$ .

$x^{4} \frac{z^{7} z^{5} (81 (x^{2}))}{175}$

Step 7.4.2

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

$x^{4} \frac{z^{7 + 5} (81 (x^{2}))}{175}$

Step 7.4.3

Add $7$ and $5$ .

$x^{4} \frac{z^{12} (81 (x^{2}))}{175}$

Step 7.5

Combine $x^{4}$ and $\frac{z^{12} (81 (x^{2}))}{175}$ .

$\frac{x^{4} (z^{12} (81 (x^{2})))}{175}$

Step 7.6

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

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Step 7.6.1

Move $x^{2}$ .

$\frac{x^{2} x^{4} (z^{12} \cdot (81))}{175}$

Step 7.6.2

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

$\frac{x^{2 + 4} (z^{12} \cdot (81))}{175}$

Step 7.6.3

Add $2$ and $4$ .

$\frac{x^{6} (z^{12} \cdot (81))}{175}$

Step 8

Move $81$ to the left of $x^{6} z^{12}$ .

$\frac{81 x^{6} z^{12}}{175}$