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HomeMathWhat are Exponents ? Definition, Examples, and Quiz

What are Exponents ? Definition, Examples, and Quiz


Exponents could make your math issues quite a bit simpler to deal with. Merely put, it’s a shortcut for multiplying numbers time and again.


Take a look at the next multiplication downside:

8 × 8 × 8 × 8 × 8 × 8

As an alternative of multiplying 8 six instances by itself, we will simply write 86 and it’ll imply the identical factor.

When studying 86, we are saying eight to the sixth energy or eight to the ability of six.

In an analogous manner,

12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 × 12 = 1210

In 1210, 12 is named the bottom and 10 is named the exponent.

Different examples of exponents:

53 = 5 × 5 × 5

94 = 9 × 9 × 9 × 9

72 = 7 × 7

66 = 6 × 6 × 6 × 6 × 6 × 6 × 6

28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Basically,

yn = y × y × y × y ×…× y × y  (n instances)

In one of many examples above, it says 72 = 7 × 7

What would you say 71 is the same as?

For 72, you wrote down 7 twice.

Subsequently, for 71, you’ll write down 7 as soon as and naturally there isn’t a must have a multiplication signal.

71 = 7

Frequent pitfalls to keep away from when working with exponents:

What’s -26 equals to?

Is it equal to -2 × -2 × -2 × -2 × -2 × -2 ?

Or is it equal to -(2 × 2 × 2 × 2 × 2 × 2) ?

It is the same as -(2 × 2 × 2 × 2 × 2 × 2) = -(26) = – 64

Nevertheless, (-2)6 is a unique story.

(-2)6 = (-2) × (-2) × (-2) × (-2) × (-2) × (-2) = – × – × – × – × – × – × 2 × 2 × 2 × 2 × 2 × 2

Discover that – × – = +

So, – × – × – × – × – × – × 2 × 2 × 2 × 2 × 2 × 2 = + × + × + × 26

Word that + × + = +

(-2)6 = +26

In (-2)6, the exponent is even. Change it to any odd quantity and the reply can be damaging.

(-2)7 = (-2) × (-2) × (-2) × (-2) × (-2) × (-2)× (-2) = – × – × – × – × – × – × – × 2 × 2 × 2 × 2 × 2 × 2 × 2

– × – × – × – × – × – × – × 2 × 2 × 2 × 2 × 2 × 2 × 2 = + × + × + × – × 27

+ × + × + × – × 27 = + × – × 27

Word that + × – = –

+ × – × 27 = -27

Necessary observations about exponents:

  • (-a)n is both damaging or optimistic. It’s optimistic if n is an excellent quantity. It’s damaging if n is an odd quantity.
  • -an isn’t all the time equal to (-a)n
  • -an could equal to (-a)n solely when n is an odd quantity.

What if the bottom is a fraction?

When the bottom is a fraction it is not uncommon to make use of parentheses as proven beneath:

two-thirds to the third power
The above can be equal to  

8
/
27

Exponents quiz to examine your understanding of this lesson.




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