For problems 19-23 apply the properties of exponents to determine the value of t. 19. 8^0cdot 8^2=8^t 20. (-9)^3(-9)^t=(-9)^3 21. ((3)/(8))^0((3)/(8))^t=((3)/(8))^11 22. 2^5cdot 2^0=t 23. (-0.25)^0(-0.25)^t=1

1. Apply the Zero Exponent Property ### 8^0 = 1 because any non-zero number raised to the power of zero is 1. ## Step2: Use the Product of Powers Property ### 8^0 \cdot 8^2 = 8^{0+2} = 8^2. Therefore, t = 2. # Answer: ### t = 2 --- # Explanation: ## Step1: Simplify Using the Identity Property ### (-9)^3 \cdot (-9)^t = (-9)^3. Since both sides are equal, t must be 0. # Answer: ### t = 0 --- # Explanation: ## Step1: Apply the Zero Exponent Property ### (\frac{3}{8})^0 = 1. ## Step2: Use the Product of Powers Property ### 1 \cdot (\frac{3}{8})^t = (\frac{3}{8})^{11} implies (\frac{3}{8})^t = (\frac{3}{8})^{11}. Therefore, t = 11. # Answer: ### t = 11 --- # Explanation: ## Step1: Apply the Zero Exponent Property ### 2^0 = 1. ## Step2: Calculate the Product ### 2^5 \cdot 1 = 2^5. Therefore, t = 2^5 = 32. # Answer: ### t = 32 --- # Explanation: ## Step1: Apply the Zero Exponent Property ### (-0.25)^0 = 1. ## Step2: Use the Product of Powers Property ### 1 \cdot (-0.25)^t = 1 implies (-0.25)^t = 1. Therefore, t = 0. # Answer: ### t = 0