Answer:
The answer is [tex]\frac{125}{243}[/tex]
Step-by-step explanation:
* Lets explain how to solve the problem
- Any number to power of zero = 1 (except 0)
- Ex: [tex]5^{0}=1[/tex] and [tex](\frac{1}{7})^{0}=1[/tex]
- If the power of a number is negative we can change it to positive
if we reciprocal the number
- Ex: [tex]3^{-2}=(\frac{1}{3})^{2}[/tex] and [tex](\frac{1}{2})^{-3}=(2)^{3}[/tex]
* Lets solve the problem
- We want to write each expression using positive exponents,
and evaluate
# [tex]2^{0}[/tex]
∵ Zero is not a positive exponent
- Change [tex]2^{0}[/tex] to 1 because 1 has positive exponent 1
∴ [tex]2^{0}=1[/tex]
# [tex]15^{3}[/tex]
- We can written it as [tex](3 × 5)^{3}[/tex]
∴ [tex]15^{3}=(5*3)^{3}=(5)^{3}(3)^{3}[/tex]
# [tex]9^{-4}[/tex]
- Change the negative exponent by reciprocal 9
∴ [tex]9^{-4}=(\frac{1}{9})^{4}[/tex]
∴[tex](\frac{1}{9})^{4}=\frac{1}{6561}[/tex]
- Lets evaluate
∵ 5³ = 125 and 3³ = 27
∴ 5³ × 3³ = 3375
∴[tex](\frac{1}{9})^{4}=\frac{1}{6561}[/tex]
∴ [tex](1)(3375)(\frac{1}{6561})=\frac{125}{243}[/tex]
∴ The answer is [tex]\frac{125}{243}[/tex]
