How do you simplify ${(5^{8})}^{3}$ $(5^8)^3$ ?

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How do you simplify ${(5^{8})}^{3}$ $(5^8)^3$ ?

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Answer 1 · 2015-09-25T22:01:57

It's $5^{24}$ $5^24$

Explanation:

Dealing with powers of powers is really simple: you only need to multiply the exponents. Namely, ${(a^{b})}^{c} = a^{b c}$ $(a^b)^c=a^{bc}$ .

This is a consequence of the fact that $a^{b} \cdot a^{c} = a^{b + c}$ $a^b * a^c = a^{b+c}$ : take your case as an example.

By definition, ${(5^{8})}^{3}$ $(5^8)^3$ means $5^{8} \cdot 5^{8} \cdot 5^{8}$ $5^8 * 5^8 * 5^8$ . According to the rule above, this expression simplifies into $5^{8 + 8 + 8}$ $5^{8+8+8}$ , which is indeed $5^{8 \cdot 3}$ $5^{8*3}$

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How do you simplify ${(5^{8})}^{3}$ $(5^8)^3$ ?

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