Step 1 of 4 · Three exponent rules
When the base is the same, combine exponents by adding (×) or subtracting (÷). For nested powers, multiply.
power of a power
(am)n = am × n
Same base + operation → combine the exponents. Multiply means +, divide means −, nested power means ×.
Step 2 of 4 · 4³ × 8²
Different bases — but both are powers of 2. Convert each, then add the exponents.
43 × 82
↓4 = 2², 8 = 2³
(22)3 × (23)2
↓power of a power: multiply exponents
26 × 26
↓same base × → add exponents
212
Step 3 of 4 · 9² × 12³
Two different primes in the mix? Group like with like after converting.
92 × 123
↓9 = 3², 12 = 2² × 3
(32)2 × (22 × 3)3
↓distribute the outer exponent; nested powers multiply
34 × 26 × 33
↓group like bases: combine the two 3's
26 × 37
Recipe: convert each base → distribute exponents → group like bases → add/sub exponents.