Question

Question
Use the Power Rule of Exponents to create a simplified equivalent expression for (194)9 .(1 point)
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Answer 1

The Power Rule of Exponents states that for any real number a and any positive integers m and n, $$a^m \cdot a^n = a^{m+n}$$

Therefore, we can apply the power rule to simplify the expression (194)^9:

(194)^9 = (194)^(6+3) = (194)^6 * (194)^3

Now, to further simplify (194)^6, we can apply the power rule again:

(194)^6 = (194)^(4+2) = (194)^4 * (194)^2

And finally, we can apply the power rule once more to simplify (194)^4:

(194)^4 = (194)^2 * (194)^2

At this point, we have simplified (194)^9 to (194)^6 * (194)^3, (194)^6 to (194)^4 * (194)^2, and (194)^4 to (194)^2 * (194)^2.

So the simplified expression for (194)^9 is:

(194)^9 = (194)^6 * (194)^3 = (194)^4 * (194)^2 * (194)^3 = (194)^2 * (194)^2 * (194)^2 * (194)^2 * (194)