Question

which of the following equations are true? (choose 3)
a $7^{6} \times 7^{-4} = 7^{2}$
b $7^{-2} \times 7^{-8} = 7^{6}$
c $7^{-7} \times 7^{3} = 7^{-4}$
d $7^{-2} \times 7^{5} = 7^{3}$
e $7^{2} \times 7^{6} = 7^{-8}$

Explanation:

Step1: Apply exponent product rule to A

When multiplying like bases, add exponents: $7^{6 + (-4)} = 7^{2}$. This matches the right side.

Step2: Apply exponent product rule to B

$7^{-2 + (-8)} = 7^{-10}$, which does not equal $7^{6}$.

Step3: Apply exponent product rule to C

$7^{-7 + 3} = 7^{-4}$. This matches the right side.

Step4: Apply exponent product rule to D

$7^{-2 + 5} = 7^{3}$. This matches the right side.

Step5: Apply exponent product rule to E

$7^{2 + 6} = 7^{8}$, which does not equal $7^{-8}$.

Answer:

A. $7^{6} \times 7^{-4} = 7^{2}$
C. $7^{-7} \times 7^{3} = 7^{-4}$
D. $7^{-2} \times 7^{5} = 7^{3}$