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## Class 8 (Old)

### Course: Class 8 (Old)>Unit 10

Lesson 2: Negative exponents

# Negative exponents

Negative exponents can be rewritten in two ways. Firstly, start with 1 and divide it by 2 the same number of times as the exponent. Secondly, take the reciprocal of the base and raise it to the positive exponent. Created by Sal Khan.

## Want to join the conversation?

• i'm confused. so at he says that 1/25/64 is just going to be 64/25 but never explained why? How did he reach that conclusion? i'm so lost! •  I assume it is 1/(25/64), and to divide fractions, you reciprocate (flip) the one in the denominator and multiply, so 1 * 64/25 = 64/25. If it were (1/25)/64, then that would be a different answer 1/25 * 1/64.
• I'm confused. If for example 2^4 is 2*2*2*2=16, why is 2^-4 meaning 2/2/2/2 equal to 1/4 rather than 1/16? •  Negative exponents move the value to the other side of a division sign, so 2^-4/1 makes it 1/2^4. Exponents are a shortcut for multiplication, not division. • An exponent says how many times to use the base in multiplication. So for example, 2^2 = 2 x 2 = 4.

3^5 = 3 x 3 x 3 x 3 x 3 = 243

Intuitively thinking based on the above: 2^-2:

How does a negative exponent become a reciprocal? That doesn't make sense to me yet. • It's based on exponent rules. 3^2 x 3^3 would be (3 x 3) x (3 x 3 x 3), or 3^5. So for multiplication of two exponents with the same bases, you add the exponents. What about division? 3^3 / 3^2 is (3 x 3 x 3) / (3 x 3), so it would be 3/1, or 3, which is 3^1. So for division with the same base, you subtract the exponent. If you have 3^3 / 3^3, you would have 3^(3-3) = 3^0 because of this rule, so 3^0 = 3^3/3^3, which turns out to be 1. Anything to the 0th power is 1. if you take 3^0 / 3^1, you have 3^-1, which is also 1/3, so it's the reciprocal. I hope this makes sense to you.
• I think a negative exponent is basically the reciprocal of the positive reciprocal. Is this right? • "1 over 25/64 is just going to be 64/25".

Why?

Please explain this in detail (or provide a link to a lesson on this). I do not understand. • Is there any other way to understand 2 to the power of -4 and, what this negative symbol does? • The negative sign on an exponent means the reciprocal. Think of it this way: just as a positive exponent means repeated multiplication by the base, a negative exponent means repeated division by the base.

So 2^(-4) = 1/(2^4) = 1/(2*2*2*2) = 1/16. The answer is 1/16.

Have a blessed, wonderful New Year!
• I've always been so confused on negative exponents, this helped me a lot!
But I don't understand how 1/(25/64)=64/25? • I asked chatgpt about it and this is the answer it returned. This helped me a lot!

(this is just the excerpt that helped me)
Now, let's consider a fraction like a/b, where "a" is the numerator and "b" is the denominator. Dividing by this fraction means we are asking how many times a fraction with value (a/b) fits into the dividend.

Let's use the dividend "1" for our example: 1 / (a/b).

To determine how many times the fraction (a/b) fits into 1, we can rephrase the question as "what number, when multiplied by (a/b), gives us 1?" In other words, we want to find the multiplicative inverse of (a/b) that, when multiplied, yields 1.

The multiplicative inverse of a fraction a/b is its reciprocal, which is b/a. Why? Because when you multiply a fraction by its reciprocal, the result is always 1.
• REALLY CONFUSED! Ok i don't get how you calculate 2^-4 how do you do that. It makes no sense to me?  