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July 22, 2014

July 22, 2014

Posted by **Eve** on Thursday, September 10, 2009 at 8:18pm.

- Algebra -
**MathMate**, Thursday, September 10, 2009 at 8:38pmFirst, you'd have to adhere to the rules of priority.

The expression 64^{2/3}is much clearer.

The 2 in the exponent requires us to square the base, and the 3 in the denominator represents (1/3) means we need to take the cube root of the base.

So whether you do ∛((64)²) or (∛64)³ will give the same answer, i.e. ∛(4096)=16 or (4)²=16. The 4 comes from the cube root of 64, or 64^{1/3}.

For 11^{-3/2}it is the same procedure, by following the laws of exponents:

x^{a+b}= x^{a}× x^{b}

x^{ab}= (x^{a})^{b}

x^{-a}= 1/x^{a}

x^{1/a}= ath root of x.

Therefore

11^{-3/2}

=1/11^{3/2}

=1/∛(11³)

=1/∛(1331)

- Algebra-correction -
**MathMate**, Thursday, September 10, 2009 at 8:39pm11

^{-3/2}

=1/11^{3/2}

=1/√(11³)

=1/√(1331)

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