What is (4^3)^n+(4^3)^n ?

The solution to (4^3)^n+(4^3)^n is 2^{1+6n}

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simplify (4^3)^n+(4^3)^n

simplify

(4^{3})^{n} + (4^{3})^{n}

2^{1 + 6 n}

Solution steps

(4^{3})^{n} + (4^{3})^{n}

Add similar elements:

(4^{3})^{n} + (4^{3})^{n} = 2 (4^{3})^{n}

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

Apply exponent rule:

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

(4^{3})^{n} = (4^{3})^{n}

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

4^{3} = 64

= 2 \cdot 6 4^{n}

Factor the number:

64 = 2^{6}

= 2 (2^{6})^{n}

Apply exponent rule:

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

(2^{6})^{n} = 2^{6 n}

= 2 \cdot 2^{6 n}

Apply exponent rule:

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

2 \cdot 2^{6 n} = 2^{1 + 6 n}

= 2^{1 + 6 n}

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