Write the Fraction in Simplest Form (15b^10)/((5b^5)^2)

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

Step 1

Simplify the denominator.

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

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

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

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

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

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

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

Multiply $5$ by $2$ .

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

Step 2

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{5}$