1.

Simplify and write in exponentied form of(3⁵÷3⁸)⁵×3-⁵​

Answer»

er: 3^{-20} or \frac{1}{3^{20}}

Step-by-step explanation:

(3^{5} ÷ 3^{8} × 3^{-5} = (\frac{3^{5} }{3^{8} } )^{5} × [tex]\frac{1}{3^{5} }

=(3^{5-8})^{5} × \frac{1}{3^{5} } (I USED the indices law of division, which in turn became subtraction. ) For the 3^{-5}, -5 is a raised power and can be turned to a fraction if BROUGHT down.

=By SIMPLIFYING the above EQUATION, you get this: (3^{-3} )^{5} × \frac{1}{3^{5} }

= If I break this further, -3 and 5 as powers will multiply each other, that is the indices law of power and the other fraction of \frac{1}{3^{5} }, will be dividing the first expression THUS:

(3)^{-3×5} × \frac{1}{3^{5} } \\=\frac{3^{-15}}{3^5}\\

At this step, apply Indices law of division, and as they have the same base, the powers of numerator and denominator will subtract each other. Thus your final answer:

= 3^{-15-5} \\=3^{-20}


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