What is \sqrt[4]{400^3} ?

The solution to \sqrt[4]{400^3} is 40sqrt(5)

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simplify \sqrt[4]{400^3}

simplify

405

Decimal Notation

89.44271 \dots

Solution steps

Apply radical rule:

= (40 0^{3})^{\frac{1}{4}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 40 0^{3 \cdot \frac{1}{4}}

3 \cdot \frac{1}{4} = \frac{3}{4}

= 40 0^{\frac{3}{4}}

40 0^{\frac{3}{4}} = 2 0^{\frac{3}{2}}

= 2 0^{\frac{3}{2}}

2 0^{\frac{3}{2}} = (25)^{3}

= (25)^{3}

Apply exponent rule:

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

= 2^{3} (5)^{3}

(5)^{3} : 5^{\frac{3}{2}}

= 2^{3} \cdot 5^{\frac{3}{2}}

5^{\frac{3}{2}} = 55

= 2^{3} \cdot 55

2^{3} = 8

= 8 \cdot 55

Multiply the numbers:

8 \cdot 5 = 40

= 405

(1.96)^{2} \cdot 0.5 \cdot 0.5

e^{- 2 t} e^{2 t}

1.4 \cdot 1.42 \cdot (\frac{1885}{331}) \cdot 1.5 \cdot 1 0^{- 5}

x + 9 \cdot x + 8