Question

Three questions, 38 points

simplify the first picture


second question

simplify the second picture

third question

simplify the third picture

Answer 1

The rules of exponents that apply here are ...

`a^(b)\cdot a^(c)=a^((b+c))\\a^(-b)=(1)/(a^b)\\ \left(a^(b)\right)^(c)=a^((b\cdot c))`

1.

`\displaystyle \left((4^(7))/(5^(2))\right)^(3)=(4^((7\cdot 3)))/(5^((2\cdot 3)))\\\\=(4^(21))/(5^(6))`

2.

`\displaystyle (9^(2))/(9^(7))=9^((2-7))=9^(-5)\\\\=(1)/(9^5)`

3.

`\displaystyle (6^(-3))/(6^(5))=6^((-3-5))=6^(-8)\\\\=(1)/(6^8)`