Question

Evaluate each expression for the given value(s) of the variables(s).

Answer 1

`\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}`

Question : 9

plugging the value of x as 10, we get

`\longrightarrow\: \: x {}^( - 4)`

`\longrightarrow\: 10 {}^( - 4)`

`\longrightarrow \frac{1}{10 {}^(4) }`

`\longrightarrow(1)/(10000)`

`\longrightarrow0.0001`

Question : 10

plugging the value of

• a as 6
• b as 3

`\longrightarrow2 {a}^( - 1) b {}^( - 3)`

`\longrightarrow2 * 6 {}^( - 1) * 3 {}^( - 3)`

`\longrightarrow (2)/(6 * 27)`

`\longrightarrow (2)/(162)`

`\longrightarrow (1)/(81)`

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Answer 2

9.
`(1)/(10,000) = 0.0001`

10.
`(1)/(81)`

Explanation:

9.
`x^(-4)`

Evaluate when x = 10.

Substitute x = 10 into the expression

`10^(-4)`

Apply the negative exponent rule (
`a^(-n) = (1)/(a^n)`)

Thus:

`= (1)/(10^4)`

`= (1)/(10^4) = (1)/(10,000) = 0.0001`

10.
`2a^(-1)b^(-3)`

Evaluate when a = 6 and b = 3

Substitute

`(2*6^(-1))(3^(-3))`

Apply the negative exponent rule

`(2*(1)/(6))((1)/(3^3))`

`((2)/(6))((1)/(27))`

`(2*1)/(6*27)`

`(1)/(81)`