Hello!
The answer are:
- Product of powers.
- Power of a power.
- Negative exponents.
Why?
Let's solve it!
It's a math rule that we must solve first what's into brakers or parenthesis, so,
First: Product of powers [tex][(7)^{5}*(7)^{3}][/tex]
According to the exponent's law(produc of power property)we need to sum the exponents and keep the base
Exponents: 5 and 3
Base: 7
Applying it we have:
[tex](7)^{5+3}=(7)^{8}[/tex]
Then, we can apply the power of a power property.
The power of a power property state that we must keep the same base and then multiply the exponents:
[tex][(7)^{5}*(7)^{3}]^{-4}[/tex]
Exponents are:
3
-4
So,
[tex](7)^{8*-4}=(7)^{-32}[/tex]
Finally, we apply the negative exponents property, negative exponents are the reciprocal of the positive exponents,
So, we will have that:
[tex](7)^{-32}=\frac{1}{7^{32} }[/tex]
Have a nice day!
