Algebra
Rules of Exponents
If \( 3 ^ N = 3 ^ 5 \times 3 ^ 4\), what is the value of \(N\)?
What value of \(N\) satisfies the equation
\[ \frac { 8 ^ {22}} { 8 ^ {11}} = 8 ^ N? \]
Given \(3^N = 9 ^{10} \), what is the value of \(N\)?
Hint: Rewrite 9 as \(3^2.\)
If \(x\) is a real number satisfying \( 14 ^x = 3 \), what is the value of \( 14 ^{2x + 1} ?\)
\(x\) and \(y\) satisfy \(2^x = 10\) and \(10 ^ y = 128\). What is the value of \(xy\)?
Hint: Rewrite the "10" in \(10^y = 128\) by using the fact that \(2^x = 10.\)