Question

Write the following expressions as an exponential term with a single base: 2²·2³·( 2/3 )^−2

a. 2⁵⋅3^−2
b. 2³⋅3²
c. 2^−1⋅3^−2
d. 2²⋅3^−2

Answer 1

To write the given expressions as an exponential term with a single base, simplify each expression and express it using exponentiation. The final expressions are: 2^5 * (2/3)^(-2a), 2⁵⋅3^(-2b), 2^3 * 3^2, 2^(-1) * 3^(-2), and 2^2 * 3^(-2).

Step-by-step explanation:

To write the given expressions as an exponential term with a single base, we need to simplify each expression first.

1. 2²·2³·( 2/3 )^(-2a) = (2^2)(2^3)(2/3)^(-2a) = 2^(2+3) * (2/3)^(-2a) = 2^5 * (2/3)^(-2a)
2. 2⁵⋅3^(-2b) remains as it is since it is already written in exponential form.
3. 2³⋅3² = (2^3)(3^2) = 2^3 * 3^2
4. 2^-1⋅3^-2 = (1/2)(1/3^2) = 2^(-1) * 3^(-2)
5. 2²⋅3^-2 = (2^2)(1/3^2) = 2^2 * 3^(-2)

The final expressions as a single exponential term with a base are: