Question

Which expression is equivalent to (StartFraction 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline EndFraction) Superscript one-half?.

Answer 1

The expression is equivalent to 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline is,

$x=2$

What is equivalent expression?

Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.

Given information-

The expression given in the problem is,

$\left((4^{\dfrac{5}{4}}\times4^{\dfrac{1}{4}}\div 4^{\dfrac{1}{2}} \right)^{\frac{1}{2}}$

Let the result of the given expression is x. Rewrite the given expression as,

$x=\left(\dfrac{4^{\dfrac{5}{4}}\times4^{\dfrac{1}{4}}}{4^{\dfrac{1}{2}}} \right)^{\frac{1}{2}}$

When the two number is multiplies with the same base, the powers of the number is added in result. Thus,

$x=\left(\dfrac{4^{(\dfrac{5}{4}+\dfrac{1}{4})}}{4^{\dfrac{1}{2}}} \right)^{\frac{1}{2}}\\x=\left(\dfrac{4^{(\dfrac{3}{2})}}{4^{\dfrac{1}{2}}} \right)^{\frac{1}{2}}$

When the two number is divided with the same base, the powers of the number is subtracted in result. Thus,

$x=\left(4^{\dfrac{3}{2}-\dfrac{1}{2}} \right)^{\frac{1}{2}}$

$x=\left(4^1} \right)^{\frac{1}{2}}\\x=\left(4} \right)^{\frac{1}{2}}\\x=(2^2)^{\dfrac{1}{2}} \\x=2$

Thus the expression is equivalent to 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline is,

$x=2$

Learn more about the equivalent expression here;

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