Algebra Examples

$\frac{5 b}{8 a^{3}} = \frac{x}{24 a^{3} b^{2}}$

Step 1

Rewrite the equation as $\frac{x}{24 a^{3} b^{2}} = \frac{5 b}{8 a^{3}}$ .

$\frac{x}{24 a^{3} b^{2}} = \frac{5 b}{8 a^{3}}$

Step 2

Multiply both sides by $24 a^{3} b^{2}$ .

$\frac{x}{24 a^{3} b^{2}} (24 a^{3} b^{2}) = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{x}{24 a^{3} b^{2}} (24 a^{3} b^{2})$ .

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Step 3.1.1.1

Rewrite using the commutative property of multiplication.

$24 \frac{x}{24 a^{3} b^{2}} (a^{3} b^{2}) = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3.1.1.2

Cancel the common factor of $24$ .

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Step 3.1.1.2.1

Factor $24$ out of $24 a^{3} b^{2}$ .

$24 \frac{x}{24 (a^{3} b^{2})} (a^{3} b^{2}) = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3.1.1.2.2

Cancel the common factor.

$24 \frac{x}{24 (a^{3} b^{2})} (a^{3} b^{2}) = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{x}{a^{3} b^{2}} (a^{3} b^{2}) = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3.1.1.3

Cancel the common factor of $a^{3} b^{2}$ .

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Step 3.1.1.3.1

Cancel the common factor.

$\frac{x}{a^{3} b^{2}} (a^{3} b^{2}) = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3.1.1.3.2

Rewrite the expression.

$x = \frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{5 b}{8 a^{3}} (24 a^{3} b^{2})$ .

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Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$x = 24 \frac{5 b}{8 a^{3}} (a^{3} b^{2})$

Step 3.2.1.2

Cancel the common factor of $8$ .

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Step 3.2.1.2.1

Factor $8$ out of $24$ .

$x = 8 (3) \frac{5 b}{8 a^{3}} (a^{3} b^{2})$

Step 3.2.1.2.2

Factor $8$ out of $8 a^{3}$ .

$x = 8 (3) \frac{5 b}{8 (a^{3})} (a^{3} b^{2})$

Step 3.2.1.2.3

Cancel the common factor.

$x = 8 \cdot 3 \frac{5 b}{8 a^{3}} (a^{3} b^{2})$

Step 3.2.1.2.4

Rewrite the expression.

$x = 3 \frac{5 b}{a^{3}} (a^{3} b^{2})$

Step 3.2.1.3

Combine $3$ and $\frac{5 b}{a^{3}}$ .

$x = \frac{3 (5 b)}{a^{3}} (a^{3} b^{2})$

Step 3.2.1.4

Multiply $5$ by $3$ .

$x = \frac{15 b}{a^{3}} (a^{3} b^{2})$

Step 3.2.1.5

Cancel the common factor of $a^{3}$ .

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Step 3.2.1.5.1

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

$x = \frac{15 b}{a^{3}} (a^{3} (b^{2}))$

Step 3.2.1.5.2

Cancel the common factor.

$x = \frac{15 b}{a^{3}} (a^{3} b^{2})$

Step 3.2.1.5.3

Rewrite the expression.

$x = 15 b \cdot b^{2}$

Step 3.2.1.6

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

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Step 3.2.1.6.1

Move $b^{2}$ .

$x = 15 (b^{2} b)$

Step 3.2.1.6.2

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

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Step 3.2.1.6.2.1

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

$x = 15 (b^{2} b^{1})$

Step 3.2.1.6.2.2

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

$x = 15 b^{2 + 1}$

Step 3.2.1.6.3

Add $2$ and $1$ .

$x = 15 b^{3}$