Basic Math Examples

$\frac{p \cdot 29 \cdot 45^{2}}{12} \cdot (\frac{p \cdot 45^{2}}{8})$

Step 1

Combine.

$\frac{p \cdot 29 \cdot 45^{2} (p \cdot 45^{2})}{12 \cdot 8}$

Step 2

Multiply $p$ by $p$ by adding the exponents.

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Step 2.1

Move $p$ .

$\frac{p \cdot p \cdot 29 \cdot 45^{2} \cdot 45^{2}}{12 \cdot 8}$

Step 2.2

Multiply $p$ by $p$ .

$\frac{p^{2} \cdot 29 \cdot 45^{2} \cdot 45^{2}}{12 \cdot 8}$

Step 3

Multiply $45^{2}$ by $45^{2}$ by adding the exponents.

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Step 3.1

Move $45^{2}$ .

$\frac{p^{2} \cdot 29 \cdot (45^{2} \cdot 45^{2})}{12 \cdot 8}$

Step 3.2

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

$\frac{p^{2} \cdot 29 \cdot 45^{2 + 2}}{12 \cdot 8}$

Step 3.3

Add $2$ and $2$ .

$\frac{p^{2} \cdot 29 \cdot 45^{4}}{12 \cdot 8}$

Step 4

Simplify the numerator.

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Step 4.1

Raise $45$ to the power of $4$ .

$\frac{p^{2} \cdot 29 \cdot 4100625}{12 \cdot 8}$

Step 4.2

Multiply $4100625$ by $29$ .

$\frac{p^{2} \cdot 118918125}{12 \cdot 8}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Multiply $12$ by $8$ .

$\frac{p^{2} \cdot 118918125}{96}$

Step 5.2

Cancel the common factor of $118918125$ and $96$ .

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Step 5.2.1

Factor $3$ out of $p^{2} \cdot 118918125$ .

$\frac{3 (p^{2} \cdot 39639375)}{96}$

Step 5.2.2

Cancel the common factors.

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Step 5.2.2.1

Factor $3$ out of $96$ .

$\frac{3 (p^{2} \cdot 39639375)}{3 (32)}$

Step 5.2.2.2

Cancel the common factor.

$\frac{3 (p^{2} \cdot 39639375)}{3 \cdot 32}$

Step 5.2.2.3

Rewrite the expression.

$\frac{p^{2} \cdot 39639375}{32}$

Step 5.3

Move $39639375$ to the left of $p^{2}$ .

$\frac{39639375 p^{2}}{32}$