What is expand 64^2*8^4 ?

The solution to expand 64^2*8^4 is 16777216

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expand 64^2*8^4

expand

6 4^{2} \cdot 8^{4}

16777216

Solution steps

6 4^{2} \cdot 8^{4}

Factor integer

64 = 2^{6}

= (2^{6})^{2} \cdot 8^{4}

Apply exponent rule:

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

(2^{6})^{2} = 2^{6 \cdot 2}

= 2^{6 \cdot 2} \cdot 8^{4}

Refine

= 2^{12} \cdot 8^{4}

Factor integer

8 = 2^{3}

= 2^{12} (2^{3})^{4}

Apply exponent rule:

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

(2^{3})^{4} = 2^{3 \cdot 4}

= 2^{12} \cdot 2^{3 \cdot 4}

Refine

= 2^{12} \cdot 2^{12}

Apply exponent rule:

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

2^{12} \cdot 2^{12} = 2^{12 + 12}

= 2^{12 + 12}

Add the numbers:

12 + 12 = 24

= 2^{24}

2^{24} = 16777216

= 16777216

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