Question

which expression is not equal to the expression shown? $3^{3} \div 3^{-4}$ $3^{-3} \div 3^{4}$ $3^{7} \div 3^{0}$ $3 \times 3^{6}$ $3^{3} \times 3^{4}$

Explanation:

Step1: Simplify the original expression

Use exponent rule: $a^m \div a^n = a^{m-n}$
$3^3 \div 3^{-4} = 3^{3 - (-4)} = 3^{3+4} = 3^7$

Step2: Simplify Option 1

Use exponent rule: $a^m \div a^n = a^{m-n}$
$3^{-3} \div 3^4 = 3^{-3-4} = 3^{-7} = \frac{1}{3^7}$

Step3: Simplify Option 2

Use exponent rule: $a^0=1$ and $a^m \div a^n = a^{m-n}$
$3^7 \div 3^0 = 3^{7-0} = 3^7$

Step4: Simplify Option 3

Use exponent rule: $a^m \times a^n = a^{m+n}$
$3 \times 3^6 = 3^{1+6} = 3^7$

Step5: Simplify Option 4

Use exponent rule: $a^m \div a^n = a^{m+n}$ (rewriting division as multiplication)
$3^3 \times 3^4 = 3^{3+4} = 3^7$

Answer:

A. $3^{-3} \div 3^4$