Sec 3 · G1 (N(T))

Index notation

Practise index notation with step-by-step help. Free account.

1. Base and index

Write repeated factors as powers

\displaystyle 2 \times 2 \times 2 \times 7 \times 7

e.g.

\displaystyle 2 \times 2 \times 2 \times 7 \times 7

\displaystyle = 2^{3} \times 7^{2}

\displaystyle = 392

Work out each power first

\displaystyle 3^{3} - 2^{4}

e.g.

\displaystyle 3^{3} - 2^{4}

\displaystyle = 27 - 16

\displaystyle = 11

📖 Worked example

Write $2 \times 2 \times 11 \times 11 \times 11$ in index notation.

Step 1 of 1

The base is the number multiplied; the index is how many times it is multiplied

2 \times 2 \times 11 \times 11 \times 11 = 2^2 \times 11^3

📖 Worked example

Evaluate $-3^5$ .

Step 1 of 2

What does it mean? Look for a bracket

-3^5 = -(3 \times 3 \times 3 \times 3 \times 3)

📖 Worked example

Evaluate $3^2 \times 2^4$ .

Step 1 of 2

Work out each power first

3^2 = 3 \times 3

= 9

2^4 = 2 \times 2 \times 2 \times 2

= 16

Practise index notation with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

1. Base and index

Write repeated factors as powers

\displaystyle 2 \times 2 \times 2 \times 7 \times 7

e.g.

\displaystyle 2 \times 2 \times 2 \times 7 \times 7

\displaystyle = 2^{3} \times 7^{2}

\displaystyle = 392

Work out each power first

\displaystyle 3^{3} - 2^{4}

e.g.

\displaystyle 3^{3} - 2^{4}

\displaystyle = 27 - 16

\displaystyle = 11

📖 Worked example

Write $2 \times 2 \times 11 \times 11 \times 11$ in index notation.

Step 1 of 1

The base is the number multiplied; the index is how many times it is multiplied

2 \times 2 \times 11 \times 11 \times 11 = 2^2 \times 11^3

📖 Worked example

Evaluate $-3^5$ .

Step 1 of 2

What does it mean? Look for a bracket

-3^5 = -(3 \times 3 \times 3 \times 3 \times 3)

📖 Worked example

Evaluate $3^2 \times 2^4$ .

Step 1 of 2

Work out each power first

3^2 = 3 \times 3

= 9

2^4 = 2 \times 2 \times 2 \times 2

= 16

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