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(-2x)3(-2x3)
\n" ); document.write( "First, we can see the above expression as the product between two factors: (-2x)3 and (-2x3).
\n" ); document.write( "Both factors are rather complex and we should first make sure we understand what each one of them stands for.
\n" ); document.write( "The first factor is (-2x)3 and since the power 3 is on top of the parentheses then the whole thing inside the parentheses need to be raised to the power of 3.
\n" ); document.write( "What we have inside the parentheses is the product of two factors, -2 and x. Whenever the product of two or more factors is raised to a certain power, the whole thing can be represented as the product of each of the factors raised to that power.
\n" ); document.write( "In other words, (ab)n = anbn. This is also true for any number of factors, for example, (abcxz)n = anbncnxnzn. So, our first factor then can be rewritten as
\n" ); document.write( "(-2)3x3, which is equivalent to -8x3 since (-2)3 = (-2)(-2)(-2) = -8.
\n" ); document.write( "Going back to the original expression, after we simplified the first factor, we now have:
\n" ); document.write( "(-2x)3(-2x3) = -8x3(-2)x3,
\n" ); document.write( "which is the product of 4 factors: -8, -2, x3 and x3.
\n" ); document.write( "The product between -8 and -2 is 16, while the product between x3 and x3 is x6. This last result is obtained by using PRODUCT rule for exponents, which states that for any m and n (xmxn=xm+n).
\n" ); document.write( "Hence,
\n" ); document.write( "(-2x)3(-2x3) = 16x6
\n" ); document.write( "By the way, PRODUCT rule for exponents can be understood by realising that xm is in fact x multiplied by itself m times, while xn is x multiplied by itself n times. Therefore, the product xmxn is in fact x multiplied by itself m times, which is further multiplied by x multiplied by itself n times. Taken all these products at once, we can see that what we have is x multiplied by itself m+n times, which can be written succinctly as xm+n. This is why xmxn = xm+n \n" ); document.write( "