Question

82. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value of each expression when x = 9, y= 8, and z= 16. In each case, the expression evaluates to a rational number.
b. 11√y2z4

Answer 1

Answer:

11yz² and when evaluating we get 22528

Step-by-step explanation:

We have the expression $11\sqrt{y^{2}z^{4} }$

We know that a square root is a 1/2 exponent, so we're going to multiply the exponents of y and z by 1/2.

$11\sqrt{y^{2}z^{4} }= 11y^{2(1/2)}z^{4(1/2)} } =11yz^{2}$

Therefore the expression is rewritten as $11yz^2$

Now we're going to evaluate this expression for y = 8 and z = 16

$11yz^{2} =11(8)(16)^2=88(256)=22528$

Thus, when evaluated the result is 22528