Step 1 of 4 · The strategy
When an expression mixes numbers and powers, factor everything into primes, then combine like bases.
- Rewrite every coefficient as a power of a prime (5, 32, 8, etc.)
- Convert each composite-base power to a prime base (4² → 2⁴, 27³ → 3⁹)
- Group like bases and add/subtract exponents
- If the result is small enough, write it as a plain number
am × an = am+n ·
a0 = 1 ·
a−k = 1/ak
Step 2 of 4 · 5 · 2⁻⁴ · 32
32 hides a power of 2. Factor it, then combine the two 2-powers.
5 · 2−4 · 32
↓factor the coefficient: 32 = 2⁵
5 · 2−4 · 25
↓same base × → add exponents: −4 + 5 = 1
5 · 21
↓2¹ = 2, then 5 × 2
10
Step 3 of 4 · 6 · 4² · 4⁻⁴
Two powers with the SAME composite base — combine first, then handle the negative exponent.
6 · 42 · 4−4
↓same base 4 × → add: 2 + (−4) = −2
6 · 4−2
↓negative exponent: 4⁻² = 1 / 4² = 1/16
6 · 1/16
↓simplify 6/16 = 3/8
3/8
Two ways to land here: combine exponents first (clean), or convert 4 → 2² and chain through primes. Either works — pick whichever is fewer steps.
Step 4 of 4 · Your turn
Evaluate the expression.
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