Final answer:
To simplify the expression (10rst⁸)*9r⁹s⁴t, multiply the coefficients and add the exponents of like bases to get 90r¹⁹s⁵t⁹.
Step-by-step explanation:
To simplify the expression (10rst⁸)*9r⁹s⁴t, we need to apply the rules of exponents, which involves multiplying the coefficients and adding the exponents of like bases.
First, multiply the coefficients: 10 * 9 = 90.
Next, add the exponents of like bases:
- For r: r¹ * r⁹ = r¹⁹
- For s: s¹ * s⁴ = s⁵
- For t: t⁸ * t¹ = t⁹
Combining all these, we have 90r¹⁹s⁵t⁹.
This is the simplified form of the expression, following the properties of exponents.