How do you simplify 4^3·4^5?

1 Answer
May 29, 2016

4^3*4^5 = 4^8 = 65536

Explanation:

For positive integer exponents we have:

x^n = overbrace(x * x * .. * x)^"n times"

Hence:

x^m * x^n = overbrace(x * x * .. * x)^"m times" * overbrace(x * x * .. * x)^"n times"

=overbrace(x * x * .. * x)^"m + n times" = x^(m+n)

So in our example:

4^3*4^5 = 4^(3+5) = 4^8

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If we know our powers of 2, then it is also helpful to use another property of exponents:

If a, b, c > 0 then:

(a^b)^c = a^(bc)

So:

4^8 = (2^2)^8 = 2^(2*8) = 2^16 = 65536

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Alternatively we could write:

4^2 = 16

4^4 = 4^2 * 4^2 = 16*16 = 256

4^8 = 4^4 * 4^4 = 256*256 = 65536