Powers · Zero & negative exponents · 6.3

Positive exponents.

A “simplified” answer usually means positive exponents only. Move every negative-exponent factor to the denominator. 3x⁻² = 3/x².

01 / THE IDEA

See it work.

Watch the method

Positive exponents only

3x⁻² = 3/x².

1 / 2
3x−23x^{-2}
1

Spot the negative exponent

A negative exponent belongs in the denominator.

3x−23x^{-2}
2

Rewrite with positive exponents

Flip the negative-exponent factors to the bottom.

=3x2= \frac{3}{x^{2}}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5 or 1/x^2.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Clean it up

The coefficient stays where it is; only the negative-exponent variable moves to the bottom with a positive exponent.

Why it works

3x⁻² = 3·(1/x²) = 3/x².

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Rewrite with positive exponents: 4z^-2

1

Spot the negative exponent

A negative exponent belongs in the denominator. 4z^-2

2

Rewrite with positive exponents

Flip the negative-exponent factors to the bottom. = 4/z^2

EX 2medium

Rewrite with positive exponents: x^-2

1

Spot the negative exponent

A negative exponent belongs in the denominator. x^-2

2

Rewrite with positive exponents

Flip the negative-exponent factors to the bottom. = 1/x^2

EX 3hard

Rewrite with positive exponents: x^-3

1

Spot the negative exponent

A negative exponent belongs in the denominator. x^-3

2

Rewrite with positive exponents

Flip the negative-exponent factors to the bottom. = 1/x^3

04 / COMMON TRAPS

Where students slip.

Trap

Moving the coefficient down too.

Fix

Only the negative-exponent factor moves; 3 stays on top.

Trap

Leaving a negative exponent in the answer.

Fix

Rewrite it as a denominator.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Rewrite with positive exponents: 2x^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
C2

Rewrite with positive exponents: 3x^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
C3

Rewrite with positive exponents: z^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
C4

Rewrite with positive exponents: 2y^-2

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
Apply

Apply (4)

A1

Rewrite with positive exponents: 2y^-2

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
A2

Rewrite with positive exponents: 2z^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
A3

Rewrite with positive exponents: 3z^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
A4

Rewrite with positive exponents: z^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
Extension

Extension (4)

E1

Rewrite with positive exponents: 2x^-2

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
E2

Rewrite with positive exponents: 3x^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
E3

Rewrite with positive exponents: x^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.
E4

Rewrite with positive exponents: 3x^-3

Need a hint?
  • Move only the negative-exponent factor down.
  • Keep the coefficient in place.