Answer:
[tex] - \frac{1}{32} [/tex]
Step-by-step explanation:
Given,
x = 2
y = - 4
Now, let's solve:
[tex] \frac{1}{ {2}^{ - 2} \: {x}^{ - 3} \: {y}^{5} } [/tex]
plug the values
[tex] \frac{1}{ {2}^{ - 2} \: {(2)}^{ - 3} \: {( - 4)}^{5} } [/tex]
A negative base raised to an odd power equals a negative
[tex] \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {( - 4}^{5}) } [/tex]
Determine the sign of the fraction
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {4}^{5} } [/tex]
Write the expression in exponential form with a base of 2
[tex] - \frac{1}{ {2}^{ - 2} \times {2}^{ - 3} \times {2}^{10} } [/tex]
Calculate the product
[tex] - \frac{1}{ {2}^{5} } [/tex]
Evaluate the power
[tex] - \frac{1}{32} [/tex]
Hope this helps...
Best regards!!
