Laws of Exponents: Why Does the Power of Zero Give 1?

What is 2 to the power of 0? The laws of exponents give the answer: multiply powers of the same base and you add the exponents, divide them and you subtract. 2³ is 8, 2² is 4, 2¹ is 2… so what is 2⁰? In Day 15 of Algebra in 30 Days, we unpack powers into tiles to see why 2³ × 2² = 2⁵ (multiplying adds the powers) and why 2⁵ ÷ 2² = 2³ (dividing subtracts them). We test these exponent rules with powers of ten and with x, and spot the trap: with different bases, like 2³ × 3², there's no shortcut. Then the division law cracks the puzzle. 2³ ÷ 2³ is 8 ÷ 8 = 1, but subtracting the powers makes it 2⁰, so the zero exponent gives 1 for any number except zero. The halving pattern agrees, and a quick quiz puts all the laws together. In this video you'll learn: • why 2³ × 2² = 2⁵ (multiply → add the powers) • why 2⁵ ÷ 2² = 2³ (divide → subtract the powers) • why any non-zero number to the power of zero is 1 0:00 The puzzle 0:35 Multiplying powers 1:25 Dividing powers 2:01 Does it always work? 2:41 Why the power of zero is one 3:21 Back to the pattern 3:43 Quick quiz 4:23 What we learned