Question

Can someone help me with this plsssss Ill give 50 points.

Answer 1

Explanation:

Using the rules of exponents:

(a^5 * a ÷ a^-3) ^-1 clear up the inside of the parens

( a^(5 + 1 ) ÷ 1 /a^3) ^-1

( a^(6 ) * a^3 )^-1

(a ^(6+3) )^-1

(a^9) ^-1

a ^ (-9) or 1 /( a^9)

Answer 2

`\sf (1)/(a^9) \text{ or } a^(-9)`.

Explanation:

To simplify the expression
`\sf (a^5 \cdot a / a^(-3))^(-1)` as a power of
`\sf a`, we can use the properties of exponents.

Remember that
`\sf a^m \cdot a^n = a^(m+n)` and
`\sf a^m / a^n = a^(m-n)`.

Let's simplify the expression step by step:

`\sf \begin{aligned} (a^5 \cdot a / a^(-3))^(-1) &=(a^(5+1) \cdot a^(-(-3)))^(-1) \\ &= (a^6 \cdot a^3)^(-1) \\&= (a^9)^(-1) \\&= a^(-(9)) \\&= (1)/(a^9)\end{aligned}`

So, the expression
`\sf (a^5 \cdot a / a^(-3))^(-1)` can be represented as
`\sf (1)/(a^9) \text{ or } a^(-9)`.