How to find patterns in exponents

Practice Questions

PSAT Math › How to find patterns in exponents

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1

If is the complex number such that , evaluate the following expression:

$i^{25}-i^{23}+i^{21}-i^{19}+i^{17}-i^{15}.\ .\ .+i$

2

Simplify 272/3.

3

If p and q are positive integrers and 27p = 9q, then what is the value of q in terms of p?

4

If and are integers and

$\left ( \frac{1}{3} \right )^{a}=27^{b}$

what is the value of $a\div b$ ?

5

Solve for

$\left ( \frac{2}{3} \right )^{x+1} = \frac{27}{8}$

6

Write in radical notation:

$\left ( x+3 \right )^{\frac{2}{3}}$

7

If $\log 2=0.301$ and $\log 3=0.477$ , then what is $\log 12$ ?

8

Express in radical form : $x^{\frac{3}{5}}$

9

Write in exponential form:

$\sqrt[3]{\left ( x-1 \right )^{2}}$

10

Which of the following statements is the same as:

$\dfrac{4^{x+2}}{2^y}$

$I)\ 2^{2x+4-y} \quad II)\ 2^{x+2} / 4^y \quad III)\ (4^x)( 4^2 )(2^{-y} )$

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