Question

83. 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:

$2^{\frac{18}{11}}$

Step-by-step explanation:

The given expression is

$\sqrt[11]{y^2z^4}$

The exponent property $\sqrt[n]{x^ay^b}=x^{a/n}y^{b/n}$

Applying this exponent property, we have

$\sqrt[11]{y^2z^4}\\\\=y^{2/11}z^{4/11}$

Now, the given numeric values are x = 9, y= 8, and z= 16

On substituting these values in the simplified expression, we get

$(2)^{2/11}(16)^{4/11}$

This can be further simplified by writing $16=2^4$

$(2)^{2/11}(2^4)^{4/11}\\\\(2)^{2/11}(2)^{16/11}$

Now, applying the product rule of exponent: $x^a\cdot x^b=x^{a+b}$

$(2)^{2/11+16/11}\\\\=2^{\frac{18}{11}}$