Question

Simplify and express the result in power notation with positive exponent

Answer 1

Answer:

3²

Step-by-step explanation:

Given expression:

$\sf (3^{-3} \div 3^{-10}) \times 3^{-5}$

Following the order of operations, carry out the calculations inside the parentheses first.

$\textsf{Apply the quotient exponent rule} \quad a^b \div a^c=a^{b-c}:$

$\implies \sf 3^{-3-(-10)} \times 3^{-5}$

$\implies \sf 3^{-3+10} \times 3^{-5}$

$\implies \sf 3^{7} \times 3^{-5}$

$\textsf{Apply the product exponent rule} \quad a^b \times a^c=a^{b+c}:$

$\sf \implies 3^{7+(-5)}$

$\sf \implies 3^{7-5}$

$\sf \implies 3^2$

Learn more about exponent rules here:

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Answer 2

$\\ \rm\Rrightarrow \dfrac{3^{-3}\times 3^{-5}}{3^{-10}}$

• a^ma^n=a^m+n
• a^m/a^n=a^m-n

$\\ \rm\Rrightarrow 3^{-3+10}\times 3^{-5}$

$\\ \rm\Rrightarrow 3^73^{-5}$

$\\ \rm\Rrightarrow 3^{7-5}$

$\\ \rm\Rrightarrow 3^2$