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?
RootIndex 16 StartRoot 4 Superscript 5 Baseline EndRoot
StartRoot 2 Superscript 5 EndRoot
2
4

Answer 1

Answer:

2

Step-by-step explanation:

The expression to simplify is:

$(\frac{4^{\frac{5}{4}}*4^{\frac{1}{4}}}{4^{\frac{1}{2}}})^\frac{1}{2}$

When same base is multiplied, we ADD exponents and when same base is divided, we SUBTRACT exponents, so we can write the expression inside the parenthesis as:

$(\frac{4^{\frac{5}{4}}*4^{\frac{1}{4}}}{4^{\frac{1}{2}}})^\frac{1}{2}\\=(4^{\frac{5}{4}+\frac{1}{4}-\frac{1}{2}})^{\frac{1}{2}}\\=(4^1)^{\frac{1}{2}}\\=4^{\frac{1}{2}}$

Now, "to the power $\frac{1}{2}$" means taking the square root, so we have:

$4^{\frac{1}{2}}\\=\sqrt{4}\\=2$

Answer 2

The expression which is , equivalent to the expression given is; 2.

The expression given is;

${(( {4}^{ \frac{5}{4} } \times {4}^{ \frac{1}{4} } ) \div {4}^{ \frac{1}{2} } )}^{ \frac{1}{2} }$

The expression given can be evaluated as follows;

• {4^((5/4) + (1/4) - (1/2))} ^(1/2)

• 4^(4/4)^(1/2)

• = 4^(1/2)

• = 2.

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