15. use a law of exponents to write an equivalent expression for (a^9 · b)^-2.
15. use a law of exponents to write an equivalent expression for (a^9 · b)^-2.
Answer
Explanation:
Step1: Apply power - of - a - product rule
The power - of - a - product rule states that ((xy)^n=x^n\cdot y^n). Here (x = a^{9}), (y = b) and (n=-2). So ((a^{9}\cdot b)^{-2}=(a^{9})^{-2}\cdot b^{-2}).
Step2: Apply power - of - a - power rule
The power - of - a - power rule states that ((x^m)^n=x^{mn}). For ((a^{9})^{-2}), we have (m = 9) and (n=-2), so ((a^{9})^{-2}=a^{9\times(-2)}=a^{-18}).
Step3: Rewrite with positive exponents
Using the rule (x^{-n}=\frac{1}{x^{n}}), we can rewrite (a^{-18}\cdot b^{-2}) as (\frac{1}{a^{18}b^{2}}).
Answer:
(\frac{1}{a^{18}b^{2}})