Question

Drag values to complete each equation.

Answer 1

the answer is in the attachment below:

Answer 2

1) The value of
`((8^3)^48^(-9))/(8^3)` is 1.

2) The value of
`(8^38^(4))/((8^2)^4)` is
`8^((-1))`.

Explanation:

Given Expressions,

1)
`((8^3)^48^(-9))/(8^3)` then

Using property of exponents
`(a^x)^y=a^(xy)`

`((8)^(12)8^(-9))/(8^3)`

Using property of exponents
`a^xa^y=a^(x+y)`

`((8)^(12-9))/(8^3)`

`\Rightarrow ((8)^(3))/(8^3)`

Using property of exponents
`(a^x)/(a^y)=a^(x-y)` and
`a^0=1`

`8^((3-3))=8^0=1`

Thus, The value of
`((8^3)^48^(-9))/(8^3)` is 1.

`((8^3)^48^(-9))/(8^3)`

2)
`(8^38^(4))/((8^2)^4)`

Now applying property of exponents
`(a^x)^y=a^(xy)` in denominator,

`(8^(3)8^(4))/(8^8)`

Using property of exponents
`a^xa^y=a^(x+y)`

`(8^(3+4))/(8^8)`

`\Rightarrow (8^(7))/(8^8)`

Using property of exponents
`(a^x)/(a^y)=a^(x-y)`

`8^((7-8))=8^((-1))`

Thus, the value of
`(8^38^(4))/((8^2)^4)` is
`8^((-1))`