please help me simplify
this exponent 24^-1a^-3/6^-2b^-2
Basically it's this right?:
(24^-1 * a^-3) / (6^-2 * b^-2)
so:
(1/24 * 1/(a^3)) / (1/(6^2) * 1/(b^2))
you should know that 6^2 = 36 so 1/(6^2) = 1/36
Now multiply:
(1/(24a^3)) / (1/(36b^2))
Then flip:
(24a^3) / (36b^2)
A helpful hint when dividing fractions:
(A/B) / (C/D) =
Think that the "inside" (a.k.a., the numbers closest to the division line) will be multiplied to create the numerator, while the "outside" will be the denominator.
= (B*C)/(A*D)
woops. i flipped that...SORRY! it becomes AD / BC
so, inside = denominator, outside = numerator
(A/B)/(C/D) =
(A/B)*(D/C) = (A*D)/(B*C)
To simplify the expression (24^-1a^-3)/(6^-2b^-2), we can apply the division rule of exponents:
First, we need to simplify the exponents separately.
For 24^-1, remember that a negative exponent means taking the reciprocal. So, 24^-1 = 1/24.
For a^-3, again, a negative exponent means taking the reciprocal. So, a^-3 = 1/a^3.
For 6^-2, the negative exponent means taking the reciprocal. So, 6^-2 = 1/6^2 = 1/36.
For b^-2, similarly, b^-2 = 1/b^2.
Now, substituting the simplified exponents, the expression becomes:
(1/24 * 1/(a^3)) / (1/36 * 1/(b^2))
Next, we can simplify further by multiplying the fractions. Remember that when dividing fractions, you can multiply the first fraction by the reciprocal of the second fraction.
So, (1/24 * 1/(a^3)) / (1/36 * 1/(b^2)) becomes:
(1/24 * (a^3/1)) / (1/36 * (b^2/1))
Now, multiply the numerators and denominators:
(a^3/24) / (b^2/36)
To divide fractions, you flip the second fraction (b^2/36) and multiply:
(a^3/24) * (36/b^2)
Now, simplify:
(a^3 * 36)/(24 * b^2)
Finally, we can simplify further by canceling out common factors:
(3 * a^3 * 12)/(2 * b^2) = (36a^3) / (2b^2) = 18a^3/b^2
Therefore, the simplified expression is 18a^3/b^2.