## What you need to know

Things to remember:

• Multiplying the original number of decimal places by the power tells you how many decimals you will have.

An exponent is a number written to the top right of a number and tells us how many times we multiply a number by itself.

$$6^2 = 6\times 6$$

$$6^3 = 6\times 6\times 6$$

$$6^4= 6\times 6\times 6\times 6$$

So, all we’re doing when we have exponents is lots of multiplications. When we do these multiplications, we refer to it as “evaluating the exponent”.

Evaluate the following exponents:

$$5^2=5\times5=25$$

$$7^3=7\times7\times7=343$$

$$8^4=8\times8\times8\times8=4096$$

Evaluating decimal numbers is a little trickier, but we have some steps that can help us.

Evaluate $0.08^3$

Step 1: Count the number of decimal places.

There are two decimal places.

Step 2: Multiply the number in Step 1 by the power in the question.

$$2\times3=6$$

This number gives how many decimal places there will be in the final answer.

Step 3: Ignore the decimal point in the original question and evaluate.

$$8^3=512$$

Step 4: Set up a number filled with 0s and as many decimal places as there were in Step 2.

0.000000

Step 5: Put the number in Step 3 into the decimal in Step 4, starting from the right.

0.000002

0.000012

0.000512

$$0.08^3=0.000512$$

Evaluate $2.3^4$

Step 1: Count the number of decimal places.

There’s one decimal places.

Step 2: Multiply the number in Step 1 by the power in the question.

$$1\times4=4$$

Step 3: Ignore the decimal point in the original question and evaluate.

$$23^4=279841$$

Step 4: Set up a number filled with 0s and as many decimal places as there were in Step 2.

0.0000

Step 5: Put the number in Step 3 into the decimal in Step 4, starting from the right.

0.0001

0.0041

0.0841

0.9841

7.9841

Although we have run out of 0s to replace, we can put the last number onto the left.

27.9841

## Example Questions

#### Question 1: Evaluate $1.7^3$.

Step 1: Count the number of decimal places.

There’s one decimal places.

Step 2: Multiply the number in Step 1 by the power in the question.

$$1\times3=3$$

Step 3: Ignore the decimal point in the original question and evaluate.

$$17^3=4913$$

Step 4: Set up a number filled with 0s and as many decimal places as there were in Step 2.

0.000

Step 5: Put the number in Step 3 into the decimal in Step 4, starting from the right.

0.003

0.013

0.913

4.913

#### Question 2: Evaluate $0.02^5$

Step 1: Count the number of decimal places.

There are two decimal places.

Step 2: Multiply the number in Step 1 by the power in the question.

$$2\times5=10$$

Step 3: Ignore the decimal point in the original question and evaluate.

$$2^5=32$$

Step 4: Set up a number filled with 0s and as many decimal places as there were in Step 2.

0.0000000000

Step 5: Put the number in Step 3 into the decimal in Step 4, starting from the right.

0.0000000002

0.0000000032