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Lucas
07-12-2013, 04:19 PM
SAT math exponents

How can I simplify the following exponential expression:

\frac{4^x 4^{2x}}{4^{3x}4^3}

Thanks!!

elizabeth
07-12-2013, 04:44 PM
SAT math Rules of Exponents

If a,b are positive numbers, x,y are real numbers and m,n are positive integers then:

1) a^{x+y}=a^x a^y Product Rule

2) (a^x)^y=a^{xy} Basic Power Rule

3) (ab)^x=a^x b^x Power Rule for a product

4) (\frac{a}{b})^x=\frac{a^x}{b^x} Power Rule for a Quotient

5) a^0=1

6) a^{-x}=\frac{1}{a^x}

7) a^{\frac{m}{n}}=\sqrt[n]{a^m}


Therefore

\frac{4^x 4^{2x}}{4^{3x}4^3}=\frac{4^{3x}}{4^{3x}4^3}=\frac{ 1}{4^3}=\frac{1}{64}

Hope these help!!:D:D

Lucas
07-12-2013, 04:45 PM
Thanks Elizabeth!!