Answer:
a) 1/27
b) 16
c) 1/8
Step-by-step explanation:
a) [tex]x^{-3/2}[/tex]
One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:
[tex]x^{-3/2}=\frac{1}{x^{3/2} }[/tex]
And now, solving for x = 9 we have:
[tex]\frac{1}{x^{3/2}}=\frac{1}{9^{3/2} } =\frac{1}{27}[/tex]
b) [tex]y^{4/3}[/tex]
This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression
[tex]y^{4/3}=8^{4/3}=16[/tex]
c) [tex]z^{-3/4}[/tex]
Using the same property we used in a) we have:
[tex]z^{-3/4}=\frac{1}{z^{3/4} }[/tex]
And now, solving for z = 16 we have:
[tex]\frac{1}{z^3/4} } =\frac{1}{16^{3/4} } =\frac{1}{8}[/tex]
