Question

Simplify and express in exponential form: 8^-1 * 3^3/ 2^-4 * 9^-2

Answer 1

Answer:

2^1* 3^7

Step-by-step explanation:

8^-1 * 3^3/ 2^-4 * 9^-2

Negative exponents move from the numerator to the denominator or from the denominator to the numerator

2^4*9^2* 3^3 /8^1  

Rewriting 9^2 as 3^2^2 = 3^4  and 8 = 2^3

2^4 * 3^3 * 3^4 / 2^3

2^4/ 2^3 = 2   and 3^3 * 3^4 = 3^(3+4) = 3^7

2* 3^7

Answer 2

Answer:

Step-by-step explanation:

$\frac{8^{-1}*3^{3}}{2^{-4}*9^{-2}}=\frac{(2^{3})^{-1} * 3^{3}}{2^{-4}*(3^{2})^{-2}}\\\\=\frac{2^{3*-1}*3^{3}}{2^{-4}*3^{2*-2}}\\\\=\frac{2^{-3}*3^{3}}{2^{-4}*3^{-4}}\\\\=2^{-3+4}*3^{3+4}\\\\=2^{1}*3^{7}\\\\=2*3^{7}$