Question

Help pls i have been stuck for long time

Answer 1

Exponent rules

`\textsf{product rule: }a^b * a^c=a^((b+c))`

`\textsf{quotient rule: }a^b / a^c=a^((b-c))`

`\textsf{power rule: }(a^b)^c=a^((b * c))`

a) Use product rule:

`3^2 * 3^x=3^((2+x))`

`\implies 3^((2+x))=3^7`

`\implies 2+x=7`

`\implies x = 5`

b) Use quotient rule:

`7^8 / 7^y=7^((8-y))`

`\implies 7^((8-y))=7^6`

`\implies 8-y=6`

`\implies y=2`

c) Use power rule:

`(q^4)^z=q^((4z))`

`\implies q^((4z))=q^(12)`

`\implies 4z=12`

`\implies z=3`