Answer:
1-4. 1
5. -8
6. [tex]\rm \frac{1}{b^4}[/tex]
7. [tex]\rm \frac{1}{4}[/tex]
8. [tex]\rm \frac{5}{y^4}[/tex]
9. [tex]\rm \frac{1}{49x^2}[/tex]
10. [tex]\rm \frac{1}{9}[/tex]
Explanation:
1-4. All quantity raised to zero is equal to one. Therefore the answer to no. 1 to no. 4 is 1.
5.
[tex]\rm -8(-3x)^0[/tex]
All quantity raised to zero is equal to one.
[tex]\implies \rm -8(1)[/tex]
[tex]\implies \boxed{-8}[/tex]
6.
[tex]\rm b^{-4}[/tex]
Apply the Negative Exponent Rule: [tex]\rm x^{-n} = \frac{1}{y}[/tex]
[tex]\implies \boxed{\rm \frac{1}{b^4}}[/tex]
7.
[tex]2^{-2}[/tex]
Apply the Negative Exponent Rule
[tex]\implies \frac{1}{2^2}[/tex]
[tex]\implies \boxed{\frac{1}{4}}[/tex]
8.
[tex]\rm 5y^{-4}[/tex]
[tex]\implies \rm 5(y^{-4})[/tex]
Apply the negative exponent rule
[tex]\implies \rm 5(\frac{1}{y^4})[/tex]
[tex]\implies \rm \boxed{\rm \frac{5}{y^4}}[/tex]
9.
[tex]\rm (7x)^{-2}[/tex]
Apply the negative exponent rule
[tex]\implies \rm \frac{1}{(7x)^2}[/tex]
[tex]\implies \boxed{\rm \frac{1}{49x^2}}[/tex]
10.
[tex](3^2)^{-2}[/tex]
[tex]\implies 9^{-2}[/tex]
Apply the negative exponent rule
[tex]\implies \frac{1}{9^2}[/tex]
[tex]\implies \boxed{\frac{1}{81}}[/tex]
