Algebra

Rules of Exponents

Rules of Exponents - Algebraic

         

If 3N=35×34 3 ^ N = 3 ^ 5 \times 3 ^ 4, what is the value of NN?

What value of NN satisfies the equation

822811=8N? \frac { 8 ^ {22}} { 8 ^ {11}} = 8 ^ N?

Given 3N=9103^N = 9 ^{10} , what is the value of NN?

Hint: Rewrite 9 as 32.3^2.

If xx is a real number satisfying 14x=3 14 ^x = 3 , what is the value of 142x+1? 14 ^{2x + 1} ?

xx and yy satisfy 2x=102^x = 10 and 10y=12810 ^ y = 128. What is the value of xyxy?

Hint: Rewrite the "10" in 10y=12810^y = 128 by using the fact that 2x=10.2^x = 10.

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