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## Radical Expressions and Equations

Combine your skills of working with exponents and manipulating expressions for radical glory.

# Warmup

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 $$2^x = 10.$$

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