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How do you simplify #(5^8)^3#?

Answer 1

It's #5^24#

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

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

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

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Answer 2

Savannah Anderson

To simplify (5^8)^3, raise 5 to the power of 8 multiplied by 3, which equals 5 to the power of 24. So, (5^8)^3 simplifies to 5^24.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.