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

`2^{(18)/(11)}`

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^{(18)/(11)}`