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Bas_tet [7]
3 years ago
7

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
Mathematics
1 answer:
alexdok [17]3 years ago
4 0

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}}

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