What is \sqrt[4]{45^3} ?

The solution to \sqrt[4]{45^3} is 3\sqrt[4]{1125}

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simplify \sqrt[4]{45^3}

simplify

4 4 5^{3}

341125

Decimal

17.37438 \dots

Solution steps

4 4 5^{3}

4 5^{3} = 91125

= 491125

Prime factorization of

91125 : 3^{6} \cdot 5^{3}

= 4 3^{6} \cdot 5^{3}

Apply exponent rule:

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

3^{6} \cdot 5^{3} = 3^{4} \cdot 3^{2} \cdot 5^{3}

= 4 3^{4} \cdot 3^{2} \cdot 5^{3}

Apply radical rule:

n ab = n a n b, a \geq 0, b \geq 0

4 3^{4} \cdot 3^{2} \cdot 5^{3} = 4 3^{4} 4 3^{2} \cdot 5^{3}

= 4 3^{4} 4 3^{2} \cdot 5^{3}

Apply radical rule:

n a^{n} = a, a \geq 0

4 3^{4} = 3

= 3 4 3^{2} \cdot 5^{3}

3^{2} = 9

= 3 4 9 \cdot 5^{3}

5^{3} = 125

= 3 4 9 \cdot 125

Multiply the numbers:

9 \cdot 125 = 1125

= 341125

l a pl a c (e^{2 t} - 36) u (t - 7)

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((\frac{2}{3})^{'})^{- 2}

155 e^{- \frac{p}{50}}

e^{- 3 s} L {\frac{e ^{(t + 3) - 2}}{5}}