Question

Do you cross-multiply and subtract the quotient with the largest value?

Answer 1

D.
`(bc^5)/(a^5^/^2d^1^/^2)`

Explanation:

As you've stated, simplifying will require us to subtract according to the rule of exponents.

Step 1: Simplify using the quotient rule of exponents:

The quotient rule of exponents says that exponents on identical bases can be subtracted to simplify a division expression

Thus, we have:

`(a^3^/^2b^3c^5)/(a^2b^1^/^3)\\ \\a^(^3^/^2^-^2^)b^(^3^-^1^/^3^)c^5\\\\a^-^1^/^2b^8^/^3c^5\\\\(b^8^/^3c^5)/(a^1^/^2)`

Side note: a^-1/2 becomes a^1/2 and moved to the denominator because we applied the negative rule of exponents which allows us to clear the negative sign in -1/2.

Step 2: Divide

Since we're dividing, we multiply by the reciprocal, which gives us:

`((b^8^/^3c^5)/(a^1^/^2)) / (a^2b^5^/^3d^1^/^2)\\\\(b^8^/^3c^5)/(a^1^/^2) *(1)/(a^2b^5^/^3d^1^/^2) \\\\(b^8^/^3c^5)/(a^2b^5^/^3d^1^/^2)`

Step 3: Apply the quotient rule for b^8/3 and b^5/3:

Now we can again apply the quotient rule for b^8/3 and b^5/3 to simplify.

This means we'll bring 5/3 to the numerator and subtract it from 8/3:

`(b^(^8^/^3^-^5^/^3^)c^5)/(a^2b^5^/^3d^1^/^2) \\\\(bc^5)/(a^2d^1^/^2)`