Pamota Thomas (Prosoning) (3x^4y^-7)^3 49 a 3x^12y^21 3^3x^12/y^21 3^3x^12y^21 3xy^2

## Step 1: Distribute the exponent<br />### We have $(3x^4y^{-7})^3$. Distribute the exponent 3 to each term inside the parentheses: $3^3 (x^4)^3 (y^{-7})^3$.<br /><br />## Step 2: Simplify the terms<br />### Calculate $3^3 = 27$. For the variables, use the power of a power rule: $(a^m)^n = a^{mn}$. So, $(x^4)^3 = x^{4 \cdot 3} = x^{12}$ and $(y^{-7})^3 = y^{-7 \cdot 3} = y^{-21}$.<br /><br />## Step 3: Combine the terms<br />### Combine the simplified terms: $27x^{12}y^{-21}$.<br /><br />## Step 4: Express with positive exponents<br />### Rewrite $y^{-21}$ with a positive exponent: $\frac{1}{y^{21}}$. Therefore, the final expression is $\frac{27x^{12}}{y^{21}}$.