INDEX LAWS

This index laws calculator simplifies powers using the main exponent rules.

It covers multiplying powers, dividing powers and power of a power.

It is useful for GCSE maths revision and algebra homework checking.

The base must stay the same for these simple laws.

Choose MULTIPLY, DIVIDE or POWER mode.

Enter the base, then enter exponent m and exponent n.

Use TAB or tap a box to change the active input.

Press ENTER to refresh the answer and working.

Multiply: a^m × a^n = a^(m+n).

Divide: a^m ÷ a^n = a^(m−n).

Power: (a^m)^n = a^(m×n).

Do not add bases. The base must be the same.

x^2 × x^5 = x^7 because the powers are added.

a^9 ÷ a^4 = a^5 because the powers are subtracted.

(y^3)^4 = y^12 because the powers are multiplied.

2^3 × 2^4 = 2^7 when the base stays as 2.

Do not add exponents when the bases are different.

Do not multiply exponents for ordinary multiplication of powers.

Do not add the bases together in index law questions.

First check the base. Then choose the correct rule.

Students use it to practise powers, indices and algebra notation.

Teachers use it for quick examples of exponent rules.

Tutors use it to explain why powers are added, subtracted or multiplied.

Parents can use it to support GCSE and KS3 homework.

When do I add powers? When multiplying terms with the same base.

When do I subtract? When dividing terms with the same base.

When do I multiply? For power-of-a-power questions.

Important: these laws require the same base.

Use these pages for connected GCSE number and algebra skills.

Index Laws Calculator helps simplify algebra powers with the same base.

It covers multiplying powers, dividing powers and raising a power to another power.

The Google-friendly folder is /index-laws-calculator/.

Canonical URL: https://teletext-tools.com/index-laws-calculator/