simplify 160^{1/2}

Solution

simplify

16 0^{\frac{1}{2}}

4 \cdot 1 0^{\frac{1}{2}}

Decimal Notation

12.64911 \dots

Solution steps

16 0^{\frac{1}{2}}

Prime factorization of

160 : 2^{5} \cdot 5

= (2^{5} \cdot 5)^{\frac{1}{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

2^{5} \cdot 5 = 2^{4} \cdot 2 \cdot 5

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

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

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

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

Multiply the numbers:

2 \cdot 5 = 10

= 4 \cdot 1 0^{\frac{1}{2}}

\frac{10 v ^{3} t ^{- 5}}{( 2 v ^{2} t ^{- 2} ) ^{- 5}}

\frac{- 8}{- 3}

\frac{1}{- \frac{1}{4}}

(2 x^{2} + x + 1) (x - 1)

4356