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 a brake or parenthesis, so,
First: Product of powers [tex][(7)^{5}*(7)^{3}][/tex]
According to the exponent's law, we have a product of powers case, so, we need to sum the exponents and keep the base
Exponents: 5 and 3
Base: 7
Applying it we have:
[tex](7)^{5+3}[/tex]
[tex](7)^{8}[/tex]
Then,
We have a power of a power case, which involves multiplying the exponents:
[tex][(7)^{5}*(7)^{3}]^{-4}[/tex]
Exponents: 3 and -4
Then,
[tex](7)^{8*-4}[/tex]
Finally, we can apply the negative exponents, the negative exponent's rules state that 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!
