Question

the simplest form of 20/4 root 1250 is​

Answer 1

simplest form of 20/4root1250

Answer 2

Answer:

$\frac{20}{\sqrt[4]{1250} }$ =  $\sqrt[4]{2^7}$

Step-by-step explanation:

To find,

The simplest form of the expression   $\frac{20}{\sqrt[4]{1250} }$

Recall the formulas

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

$(a^n)^{m}} = a^{mXn}$

$\frac{a^m}{a^n} = a^{m-n}$

Solution:

The prime factorization of 1250 = 2×5×5×5×5

= 2×5⁴

$\sqrt[4]{1250}$ = $(1250)^{\frac{1}{4} }$(by applying $\sqrt[n]{a} = a^{\frac{1}{n}$)

= $(2X5^4)^{\frac{1}{4} }$

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

= $2^{\frac{1}{4}}X(5^{4X\frac{1}{4}})$(by applying $(a^n)^{m}} = a^{mXn}$ )

= $2^{\frac{1}{4}}X5$

$\frac{20}{\sqrt[4]{1250} }$ = $\frac{20}{2^{\frac{1}{4}}X5 }$

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

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

= $2^{2-\frac{1}{4} }$(by applying $\frac{a^m}{a^n} = a^{m-n}$)

= $2^{\frac{7}{4}$

= $\sqrt[4]{2^7}$

#SPJ2