Question

2 which expression does not have the same value as \\(\frac{9^6}{9^3}\\)? \\(\bigcirc\\) a. \\(9^2 \cdot 9^1\\) \\(\bigcirc\\) b. \\(9^3\\) \\(\bigcirc\\) c. \\(9^5 \cdot 9^{-2}\\) \\(\bigcirc\\) d. \\((9^6)^3\\) 3 which of the following properties is represented by the following equation? 6 which of the following equations is true? \\(\bigcirc\\) a. \\(8^3 \cdot 8^4 = 8^{12}\\) \\(\bigcirc\\) b. \\(15^0 = 0\\) \\(\bigcirc\\) c. \\(\frac{7^8}{7^4} = 7^2\\) \\(\bigcirc\\) d. \\(5^{-2} = \frac{1}{25}\\) 7 what number completes the equation to make it a true statement? \\((2^2)^{\square} = \frac{1}{64}\\)

Explanation:

Step1: Simplify the given expression

$\frac{9^6}{9^3}=9^{6-3}=9^3$

Step2: Evaluate Option A

$9^2 \cdot 9^1=9^{2+1}=9^3$

Step3: Evaluate Option B

$9^3 = 9^3$

Step4: Evaluate Option C

$9^5 \cdot 9^{-2}=9^{5+(-2)}=9^3$

Step5: Evaluate Option D

$(9^6)^3=9^{6 \times 3}=9^{18}$

Step6: Check Option A for Q6

$8^3 \cdot 8^4=8^{3+4}=8^7
eq 8^{12}$

Step7: Check Option B for Q6

$15^0=1
eq 0$

Step8: Check Option C for Q6

$\frac{7^8}{7^4}=7^{8-4}=7^4
eq 7^2$

Step9: Check Option D for Q6

$5^{-2}=\frac{1}{5^2}=\frac{1}{25}$

Step10: Solve Q7: Rewrite right-hand side

$\frac{1}{64}=\frac{1}{2^6}=2^{-6}$

Step11: Rewrite left-hand side

$(2^2)^x=2^{2x}$

Step12: Equate exponents and solve

$2x=-6 \implies x=-3$

Answer:

Question 2: D. $(9^6)^3$
Question 6: D. $5^{-2} = \frac{1}{25}$
Question 7: $-3$