Answer :
To solve the expression [tex]\(\frac{5 y^3}{(5 y)^{-2}}\)[/tex], let's proceed step-by-step.
### Step 1: Simplify the denominator.
The denominator [tex]\((5y)^{-2}\)[/tex] can be written as:
[tex]\[ (5 y)^{-2} = \frac{1}{(5 y)^2} \][/tex]
### Step 2: Calculate [tex]\((5 y)^2\)[/tex]
[tex]\[ (5 y)^2 = 5^2 \cdot y^2 = 25 y^2 \][/tex]
### Step 3: Rewrite the expression with simplified denominator
The expression is now:
[tex]\[ \frac{5 y^3}{\frac{1}{25 y^2}} = 5 y^3 \cdot 25 y^2 \][/tex]
### Step 4: Combine the terms
Multiply the constants and add the exponents of [tex]\(y\)[/tex]:
[tex]\[ 5 \cdot 25 \cdot y^{3 + 2} = 125 \cdot y^5 \][/tex]
Therefore, the expression [tex]\(\frac{5 y^3}{(5 y)^{-2}}\)[/tex] simplifies to:
[tex]\[ \boxed{125 y^5} \][/tex]
### Step 1: Simplify the denominator.
The denominator [tex]\((5y)^{-2}\)[/tex] can be written as:
[tex]\[ (5 y)^{-2} = \frac{1}{(5 y)^2} \][/tex]
### Step 2: Calculate [tex]\((5 y)^2\)[/tex]
[tex]\[ (5 y)^2 = 5^2 \cdot y^2 = 25 y^2 \][/tex]
### Step 3: Rewrite the expression with simplified denominator
The expression is now:
[tex]\[ \frac{5 y^3}{\frac{1}{25 y^2}} = 5 y^3 \cdot 25 y^2 \][/tex]
### Step 4: Combine the terms
Multiply the constants and add the exponents of [tex]\(y\)[/tex]:
[tex]\[ 5 \cdot 25 \cdot y^{3 + 2} = 125 \cdot y^5 \][/tex]
Therefore, the expression [tex]\(\frac{5 y^3}{(5 y)^{-2}}\)[/tex] simplifies to:
[tex]\[ \boxed{125 y^5} \][/tex]
