Laws of exponents, step by step
Three rules, one question each time: two powers of the same base go in and one comes out.
The question
(4²)⁸
(4²)⁸
(4 × 4) × (4 × 4) × (4 × 4) × (4 × 4) × …
2×8=16
(4²)⁸=4¹⁶
n=16
- (4²)⁸ means 8 copies of 4², all multiplied together.
- Each copy is 2 4s, and there are 8 copies — so that is 2 × 8 = 16 of them.
- 16 4s multiplied together is 4¹⁶. So n = 16. The shortcut: a power raised to a power MULTIPLIES the exponents.
How it works.
- 01
(4²)⁸ means 8 copies of 4², all multiplied together.
- 02
Each copy is 2 4s, and there are 8 copies — so that is 2 × 8 = 16 of them.
- 03
16 4s multiplied together is 4¹⁶. So n = 16. The shortcut: a power raised to a power MULTIPLIES the exponents.