Simplify (5y^3)/((5y)^-2)

$\frac{5 y^{3}}{{(5 y)}^{- 2}}$

Step 1

Move ${(5 y)}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$5 y^{3} {(5 y)}^{2}$

Step 2

Apply the product rule to $5 y$ .

$5 y^{3} (5^{2} y^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$5 \cdot 5^{2} y^{3} y^{2}$

Step 4

Multiply $5$ by $5^{2}$ by adding the exponents.

Multiply $5$ by $5^{2}$ .

Raise $5$ to the power of $1$ .

$5^{1} \cdot 5^{2} y^{3} y^{2}$

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

$5^{1 + 2} y^{3} y^{2}$

Add $1$ and $2$ .

$5^{3} y^{3} y^{2}$

Step 5

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$5^{3} (y^{2} y^{3})$

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

$5^{3} y^{2 + 3}$

Add $2$ and $3$ .

$5^{3} y^{5}$

Step 6

Raise $5$ to the power of $3$ .

$125 y^{5}$