Question

find the value of each variable that makes the equation true.

1. $8^a = 1$

answer: $a = \square$

1. $9^4 \cdot 9^{-4} = 9^b$

answer: $b = \square$

1. $5^{-3} \cdot 2^{-3} = 10^d$

answer: $d = \square$

Explanation:

Step1: Use zero exponent rule

Any non-zero number to the power of 0 is 1. So $8^a = 8^0$, thus $a=0$.

Step2: Apply exponent product rule

When multiplying like bases, add exponents: $9^4 \cdot 9^{-6} = 9^{4+(-6)} = 9^{-2}$. Set equal to $9^b$, so $b=-2$.

Step3: Rewrite left side with base 10

Note that $5^{-3} \cdot 2^{-3} = (5 \cdot 2)^{-3} = 10^{-3}$. Set equal to $10^d$, so $d=-3$.

Answer:

1. $a=0$
2. $b=-2$
3. $d=-3$