Math With AmarA C A D E M Y

Grade 9 · Connect powers and reciprocals · 84 of 750

Connect powers and reciprocals · practice 6

Evaluate 5 raised to the integer power 3. Follow the calculation, then test the quantities in the animated example.

Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.

01 · Make a prediction

Your practice question

Evaluate 5 raised to the integer power 3.

Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.

02 · Explore the model

See the mathematical relationship move.

Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.

Watch the relationship

Paused
Connect powers and reciprocals · practice 6. Current exponent: 0. Current value: 1. Final value: 125. Scale direction: Multiply repeatedlyInteger powers as repeated scalingStart1Scale operation× 5Current result1Exponent reached: 0 of 3Final value: 125
Bases are positive integers from two to six and exponents are integers from −3 to 5. The stage boxes represent operations, not equal numerical distances. Exponent zero has no multiplication steps.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Current exponent
0
Current value
1
Final value
125
Scale direction
Multiply repeatedly

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

The mathematical idea

An integer exponent records repeated multiplication for positive powers and repeated division for negative powers. The starting value at exponent zero is one. A negative exponent forms a reciprocal and does not make a positive base negative. Starting quantities: Positive base = 5; Integer exponent = 3.

a⁰=1; aⁿ=a×…×a; a⁻ⁿ=1/aⁿ

03 · Reflect and transfer

Explain what changes and why.

Why is a negative exponent different from a negative base?

This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.