Question

Evaluate 1/2^-2x^-3y^5 for x=2 and y=-4

Answer 1

`- (1)/(32)`

Explanation:

Given,

x = 2

y = - 4

Now, let's solve:

`\frac{1}{ {2}^( - 2) \: {x}^( - 3) \: {y}^(5) }`

plug the values

`\frac{1}{ {2}^( - 2) \: {(2)}^( - 3) \: {( - 4)}^(5) }`

A negative base raised to an odd power equals a negative

`\frac{1}{ {2}^( - 2) * {2}^( - 3) * {( - 4}^(5)) }`

Determine the sign of the fraction

`- \frac{1}{ {2}^( - 2) * {2}^( - 3) * {4}^(5) }`

Write the expression in exponential form with a base of 2

`- \frac{1}{ {2}^( - 2) * {2}^( - 3) * {2}^(10) }`

Calculate the product

`- \frac{1}{ {2}^(5) }`

Evaluate the power

`- (1)/(32)`

Hope this helps...

Best regards!!