Exponent Properties
This is the answer to 34 ÷ 32?
What is 32 or 9?
Solve: √x = 5
What is x = 25?
What is i^2?
Answer: -1
Rewrite 161/2 as a radical expression and simplify.
What is the square root of 16 (equal to 4)?
True or False: √(x^2) = x
False — it's |x| because square roots are always non-negative.
Simplify: √(-16)
Answer: 4i
Simplify (x2/3)3.
What is x2?
Why does x^2 = 9 have two solutions, but √x = 3 only has one?
Squaring allows for positive and negative roots, but the square root symbol only refers to the positive root.
Add: (3 + 2i) + (1 - 5i)
Answer: 4 - 3i
Why is b1/n = nth root of b1?
Because exponent rules show that raising a number to a fractional power is the same as taking a root. It maintains consistency with integer exponent properties.
Solve and explain: √(x + 1) = 2
Square both sides: x + 1 = 4 → x = 3
Multiply: (2 + 3i)(1 - i)
Answer: 2 - 2i + 3i - 3(i^2) = 2 + i + 3 = 5 + i
Why is a-n = 1/an?
We define negative exponents this way so that the rules of exponents remain consistent, especially the rule:
am * an = am+n
Create a radical equation with no solution and explain why.
√x = -3 → No solution, since square roots cannot be negative.
Why are complex numbers shown on a plane instead of a number line?
Answer: Because they have both a real part and an imaginary part, so we need 2D space — the complex plane — where the x-axis is real and the y-axis is imaginary.