Question

choose the equivalent expression with only positive exponents?10^3 x 10^-5 × 2^-81. 10^-2 × 2^-82. 1/(10^2 × 2^8)3. 100/ 2^-104. 10^2/2^8

Answer 1

According to the Negative exponent rule, you know that:

$b^{-n}=\frac{1}{b^n}$

According to the Product of powers property, you have that:

$b^n\cdot b^m=b^{(n+m)}$

Equivalent expressions have the same value, but they are written in different forms. For this case, you have this expression:

$10^3\cdot10^{-5}\cdot2^{-8}$

Simplify it in order to find an equivalent expression. Applying the Product of powers property:

$=10^{3+(-5)}\cdot2^{-8}=10^{-2}\cdot2^{-8}$

Finally, applying the Negative exponent rule, you get this equivalent expression with only positive exponents:

$=\frac{1}{10^2\cdot2^8}$

The answer is Option 2.