Simplify the Expression: 2² × 2³ Using Laws of Exponents

When you multiply $2^2 \times 2^3$, you're really saying (2×2) × (2×2×2). Count the 2's: there are 5 total, so the answer is $2^5$. Adding exponents just counts how many times the base appears!

$2^{2+3} = 2^5 = 32$ (multiplication rule), but $2^{2 \times 3} = 2^6 = 64$ (power rule). Use addition when multiplying same bases, multiplication when raising a power to another power.

No! The rule only works when the bases are the same. For $2^2 \times 3^3$, you must calculate each part separately: $4 \times 27 = 108$.

• Add exponents: Same base multiplication ($x^a \times x^b = x^{a+b}$)
• Multiply exponents: Power of a power ($(x^a)^b = x^{a \times b}$)

Once you have $2^5$, calculate: $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$. But sometimes leaving it as $2^5$ is the preferred simplified form!