Question

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

Answer 1

Explanation:

`(8^(-1)*3^(3))/(2^(-4)*9^(-2))=((2^(3))^(-1) * 3^(3))/(2^(-4)*(3^(2))^(-2))\\\\=(2^(3*-1)*3^(3))/(2^(-4)*3^(2*-2))\\\\=(2^(-3)*3^(3))/(2^(-4)*3^(-4))\\\\=2^(-3+4)*3^(3+4)\\\\=2^(1)*3^(7)\\\\=2*3^(7)`

Answer 2

2^1* 3^7

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