Question

77. Use properties of exponents to explain why it makes sense to define 16 *1/4 as √16 4 .

Answer 1

Answer and explanation:

Given : Expression $(16)^{\frac{1}{4}}$ as $\sqrt[4]{16}$

To find : Use properties of exponents to explain why it makes sense to define expression ?

Solution :

Using property of exponent,

$x^{\frac{1}{n}}=\sqrt[n]{x}$

On comparing with given expression,

Here x=16 and n=4

$(16)^{\frac{1}{4}}=\sqrt[4]{16}$

Hence by property it defied the expression.