How do you simplify and write # 5^2 times 5^4# with positive exponents?

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Answer 1 · 2018-05-18T06:50:06

#5^6#

The first law of indices you usually learn is the one about multiplying.

'If the bases are the same and you are multiplying, add the indices.'

#x^m xx x^n = x^(m+n)#

In this case the bases are both #5#

#5^2 xx 5^4 = 5^(2+4)= 5^6#

To see why this is so, write them out in expanded form:

#5^2 xx 5^4 = (5xx5) xx (5xx5xx5xx5) = 5^6#