Macioccujx

2022-07-27

Evaluate.
$\left({3}^{4}\right)\left({3}^{-2}\right)$

Ali Harper

Expert

$\left({3}^{4}\right)\left({3}^{-2}\right)=3{\left(}^{4-2}\right)$ .................................[As ${X}^{a}\ast {X}^{b}={X}^{\left(a+b\right)}$]
$={3}^{2}$
= 9

Expert

Therefore, adding the exponents, we get: 4 + -2 = 2
Applying this information to the problem, we get: ${3}^{2}=9$.
Another way you could have done this is by remembering ${3}^{4}=\left[{3}^{2}\right]\left[{3}^{2}\right]=9×9=81$.
Now, negative exponents go in the denominator to give us:
$\frac{{3}^{4}}{{3}^{2}}=\frac{81}{9}=9$

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