Basic Math Examples

$5 a \cdot (5 a) \cdot (6 b) = 33$

Step 1

Simplify.

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Step 1.1

Multiply $5$ by $5$ .

$25 a \cdot a \cdot (6 b) = 33$

Step 1.2

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

$25 (a^{1} a) \cdot (6 b) = 33$

Step 1.3

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

$25 (a^{1} a^{1}) \cdot (6 b) = 33$

Step 1.4

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

$25 a^{1 + 1} \cdot (6 b) = 33$

Step 1.5

Add $1$ and $1$ .

$25 a^{2} \cdot (6 b) = 33$

Step 1.6

Multiply $6$ by $25$ .

$150 a^{2} \cdot b = 33$

Step 2

Divide each term in $150 a^{2} \cdot b = 33$ by $150 a^{2}$ and simplify.

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Step 2.1

Divide each term in $150 a^{2} \cdot b = 33$ by $150 a^{2}$ .

$\frac{150 a^{2} \cdot b}{150 a^{2}} = \frac{33}{150 a^{2}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $150$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{150 a^{2} \cdot b}{150 a^{2}} = \frac{33}{150 a^{2}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{a^{2} \cdot b}{a^{2}} = \frac{33}{150 a^{2}}$

Step 2.2.2

Cancel the common factor of $a^{2}$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{a^{2} \cdot b}{a^{2}} = \frac{33}{150 a^{2}}$

Step 2.2.2.2

Divide $b$ by $1$ .

$b = \frac{33}{150 a^{2}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $33$ and $150$ .

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Step 2.3.1.1

Factor $3$ out of $33$ .

$b = \frac{3 (11)}{150 a^{2}}$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $3$ out of $150 a^{2}$ .

$b = \frac{3 (11)}{3 (50 a^{2})}$

Step 2.3.1.2.2

Cancel the common factor.

$b = \frac{3 \cdot 11}{3 (50 a^{2})}$

Step 2.3.1.2.3

Rewrite the expression.

$b = \frac{11}{50 a^{2}}$