Steply

Powers, square roots, absolute value

Foundations · 24 problems, easy to harder

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How we do it

  1. Powers
  2. Plus and minus

The steps for Calculate (-2)^2 + -2^2. Every solution names its steps, so you always know what comes next.

Worked examples

Calculate 2^3 Easy

The question

Question: work out 2³.

23

1 Work out the power

2³ means 2 times 2 times 2.

23 = 2 × 2 × 2 = 8

That is 8.

= 8

So the answer is 8.

Answer
= 8

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Calculate -3^2 Medium

The question

Question: work out −3².

−32

1 Work out the power

In −3², the power is only on the 3.

The minus stays in front.

Careful!

It is not (−3)².

Without brackets, the minus stays outside.

Careful: not −32 = 9 ✗

3² means 3 times 3.

32 = 3 × 3 = 9

That is 9.

= −9

So the answer is −9.

Answer
= −9

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Calculate (-2)^2 + -2^2 Harder

The question

Question: work out (−2)² + (−2²).

(−2)2 + (−22)

1 Powers

Powers come before plus.

Order: ( ) → x² √ → × ÷ → + −

(−2)² means −2 times −2.

Minus times minus is plus.

(−2)2 = (−2) × (−2) = 4

That is 4.

= 4 + (−22)

Powers come before plus.

In −2², the power is only on the 2.

The minus stays in front.

Careful!

It is not (−2)².

Without brackets, the minus stays outside.

Careful: not −22 = 4 ✗

2² means 2 times 2.

22 = 2 × 2 = 4

That is 4.

= 4 + (−4)

2 Plus and minus

Adding a negative is the same as taking away.

+ (−) = −

So 4 + (−4) becomes 4 − 4.

= 4 − 4

4 minus 4 is 0.

= 0

So the answer is 0.

Let's look back.

First: powers.

Last: plus and minus.

Answer
= 0

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Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. 2^3
    Answer
    = 8
  2. 5^2
    Answer
    = 25
  3. 3^4
    Answer
    = 81
  4. 10^3
    Answer
    = 1000
  5. √49
    Answer
    = 7
  6. √81
    Answer
    = 9
  7. |-6|
    Answer
    = 6
  8. |4 - 9|
    Answer
    = 5
  9. 1^7
    Answer
    = 1
  10. (-3)^2
    Answer
    = 9

Medium

  1. -3^2
    Answer
    = −9
  2. (-2)^3
    Answer
    = −8
  3. 2^-3
    Answer
    = 18
  4. 5^0
    Answer
    = 1
  5. √(16 + 9)
    Answer
    = 5
  6. √16 + √49
    Answer
    = 11
  7. |-5| + |3 - 7|
    Answer
    = 9
  8. (1/2)^3
    Answer
    = 18
  9. 10^-2
    Answer
    = 1100
  10. -|-8|
    Answer
    = −8

Harder

  1. (-2)^2 + -2^2
    Answer
    = 0
  2. 3 × √16 - 2^3
    Answer
    = 4
  3. |2 - 3^2| + (-1)^3
    Answer
    = 6
  4. √(100 - 36) ÷ 2^2
    Answer
    = 2