What is (2^3)^4(3^20.2^3)^3 ?

The solution to (2^3)^4(3^20.2^3)^3 is 1.52882…

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simplify (2^3)^4(3^20.2^3)^3

simplify

(2^{3})^{4} (3^{2} 0. 2^{3})^{3}

1.52882 \dots

Solution steps

(2^{3})^{4} (3^{2} \cdot 0. 2^{3})^{3}

(2^{3})^{4} = 4096

= 4096 (3^{2} \cdot 0. 2^{3})^{3}

Apply exponent rule:

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

(3^{2} \cdot 0. 2^{3})^{3} = (3^{2})^{3} (0. 2^{3})^{3}

= 4096 (3^{2})^{3} (0. 2^{3})^{3}

(3^{2})^{3} = 729

= 4096 \cdot 729 (0. 2^{3})^{3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(0. 2^{3})^{3} = 0. 2^{3 \cdot 3}

= 4096 \cdot 729 \cdot 0. 2^{3 \cdot 3}

Multiply the numbers:

3 \cdot 3 = 9

= 4096 \cdot 729 \cdot 0. 2^{9}

0. 2^{9} = 0.000000512

= 4096 \cdot 729 \cdot 0.000000512

Multiply the numbers:

729 \cdot 0.000000512 = 0.000373248

= 4096 \cdot 0.000373248

Multiply the numbers:

4096 \cdot 0.000373248 = 1.52882 \dots

= 1.52882 \dots

4 x (7 x^{2})

(4 x^{3} y^{4}) (10 x^{2} y^{6})

e^{- t} (\frac{e ^{t} ( x - y )}{2})

4 (0.5)^{- 2}

0.5 \cdot 1 0^{- 1}