## Week 2 – Math 10

This week I learned how negative exponents work and how they effect their base’s. Negative exponents unlike positive exponents don’t increase the numbers size. Normal exponents multiply a number over and over (ex. $3^3 = 3\cdot3\cdot3 = 27$) and negative exponents turn the number into a fraction (ex $3^{-3} = \frac{1}{27}$).

You can turn it into a normal number by following the next steps. I will use $5^{-4}$ for this example.

First, if the exponent is negative, then you turn it into a fraction of $\frac{x}{1}$.

Then you put the denominator on the bottom, therefor making the exponent positive.

Alternatively, I learned that if the negative was originally on the bottom, you would then move it to the top.

Then you find out what the product of the power is and put that underneath a 1, in this case $\frac{1}{625}$

I learned that if it were for example $5x^{-4}$, then only the $x$ and its exponent would be moved to the denominator as in $\frac {5}{x^4}$

If it were $(5x)^{-4}$, then both would move to the bottom.

if it were $(5x^{-4})^{-4}$ would equal $5x^{16}$ because you multiply the exponent.