Algebra Examples

$\frac{15 b^{10}}{{(5 b^{5})}^{2}}$

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $5 b^{5}$ .

$\frac{15 b^{10}}{5^{2} {(b^{5})}^{2}}$

Step 1.2

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

$\frac{15 b^{10}}{25 {(b^{5})}^{2}}$

Step 1.3

Multiply the exponents in ${(b^{5})}^{2}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{15 b^{10}}{25 b^{5 \cdot 2}}$

Step 1.3.2

Multiply $5$ by $2$ .

$\frac{15 b^{10}}{25 b^{10}}$

$\frac{15 b^{10}}{25 b^{10}}$

$\frac{15 b^{10}}{25 b^{10}}$

Step 2

Cancel the common factor of $15$ and $25$ .

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Step 2.1

Factor $5$ out of $15 b^{10}$ .

$\frac{5 (3 b^{10})}{25 b^{10}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $25 b^{10}$ .

$\frac{5 (3 b^{10})}{5 (5 b^{10})}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (3 b^{10})}{5 (5 b^{10})}$

Step 2.2.3

Rewrite the expression.

$\frac{3 b^{10}}{5 b^{10}}$

$\frac{3 b^{10}}{5 b^{10}}$

$\frac{3 b^{10}}{5 b^{10}}$

Step 3

Cancel the common factor of $b^{10}$ .

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Step 3.1

Cancel the common factor.

$\frac{3 b^{10}}{5 b^{10}}$

Step 3.2

Rewrite the expression.

$\frac{3}{5}$

$\frac{3}{5}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$