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Explanation:

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8) If the base of the exponents match on both sides of the equal sign, then the exponents can be set equal to each other.

So since (5ˣ)⁵ = 5³⁵, the base 5 is on both sides.

5(x) = 35

5x = 35

Divide by 5 on both sides to isolate the variable.

x = 7

9) Without evaluating (much) you can tell by common sense that (2⁵)(10⁵) is bigger.

The exponents are the same so you can multiply the bases. 4x5 = 20. 2 x 10 = 20. Now, just look at the exponents to see which is bigger. 5 > 4. Therefore, (2⁵)(10⁵) is bigger.

10) Nicholas's second statement is false. (2⁶)(2⁶) is the same as (2⁶)². In this case since they have the same base, you would multiply the exponents. 6 x 2 = 12. Therefore, (2⁶)(2⁶) = 2¹²