Step 1 of 4 · The rule
(23)2
The outer ² means "2 groups of" — and what's inside ( ) is 2³ = three 2s multiplied.
(aᵐ)ⁿ = a^(m × n)
multiply the exponents
Step 2 of 4 · Convert 16³ to a prime base
16 isn't prime. Factor it to a power of 2 first, then apply the rule.
163
↓first: factor the base 16 into primes
16
=
2
×
2
×
2
×
2
=
24
↓substitute 2⁴ for 16
(24)3
↓apply (aᵐ)ⁿ = a^(m × n)
24·3
↓multiply
212
Step 3 of 4 · Same rule, different prime — 9⁴
9 = 3² and the rule is the same. Watch the exponents multiply.
94
↓first: factor 9 into primes
9
=
3
×
3
=
32
↓substitute 3² for 9
(32)4
↓apply (aᵐ)ⁿ = a^(m × n)
32·4
↓multiply
38
Same recipe every time: factor the base into a prime power → multiply the exponents.
Step 4 of 4 · Your turn
25³
Pick the equivalent prime-base power.
🏆
Nice work!
You converted them all to prime bases.