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)=(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:

`=(1)/(10^2\cdot2^8)`

The answer is Option 2.