Final answer:
To simplify the expression (3x⁸y⁸)⁻³(7xy⁷), we first raise the base (3x⁸y⁸) to the power of -3. Then we multiply the result by (7xy⁷) and combine the variable terms.
Step-by-step explanation:
To simplify the expression (3x⁸y⁸)⁻³(7xy⁷), we first raise the base (3x⁸y⁸) to the power of -3.
In order to do this, we need to apply the rule that states when raising a power to another power, we multiply the exponents.
So, we get (3x⁸y⁸)⁻³ = 3⁻³x⁻²⁴y⁻²⁴.
Next, we multiply the result by (7xy⁷).
To do this, we multiply the coefficients (7 and 3⁻³) together to get 7 * 3⁻³ = 7/3³.
Finally, we combine the variable terms.
The x term has an exponent of 8 in the base and 1 in (7xy⁷), so we add the exponents to get x⁸ * x¹ = x⁹.
Similarly, the y term has exponents of 8 and 7, so we add those exponents to get y⁸ * y⁷ = y¹⁵.
Therefore, the simplified expression is (7/3³)x⁹y¹⁵.