Answer:
1. [tex]\frac{x^2}{y^3}[/tex]
2. [tex]\frac{625x^{12}}{y^8}[/tex]
3. [tex]\frac{6}{x^2y^9}[/tex]
Step-by-step explanation:
Remember, when you exponent an exponent, you multiply the powers.
When you multiply exponents, you add them.
When you divide exponents, you subtract them.
1.
Step 1: Multiply exponents
[tex]x^2y^{-3}[/tex]
Step 2: Move [tex]y^{-3}[/tex] to the denominator
[tex]\frac{x^2}{y^3}[/tex]
2.
Step 1: Multiply exponents
[tex]\frac{5^4(x^{3})^{4}}{(y^2)^4}[/tex]
Step 2: Power
[tex]\frac{625x^{12}}{y^8}[/tex]
3.
Step 1: Simplify
[tex]\frac{6x^3y^{-3}}{x^5y^6}[/tex]
Step 2: Remove terms
[tex]\frac{6y^{-3}}{x^2y^6}[/tex]
Step 3: Move [tex]y^{-3}[/tex] to the denominator
[tex]\frac{6}{x^2y^6y^3}[/tex]
Step 4: Combine like terms
[tex]\frac{6}{x^2y^9}[/tex]
