Question

Which mathematical operation should be performed to simplify the given expressions (A-D)?

A) Addition
B) Subtraction
C) Multiplication
D) Exponents

Answer 1

The mathematical operation required to simplify these expressions is exponents. Option D.

Step-by-step explanation:

To simplify expressions involving exponents, we follow a set of rules known as the laws of exponents. These rules allow us to perform operations such as adding, subtracting, multiplying, and dividing expressions with exponents.

In this case, we are given four expressions that involve exponents:

A)
`2^3 * 2^2`

B)
`5^0`

C)
`3^4 / 3^2`

D)
`x^5 / y^3`

To simplify these expressions, we use the following laws of exponents:

1. Law of Exponents: Base raised to the power of a sum (or difference) is equal to the product of the base raised to the power of each term.

Example:
`a^(^m^+^n^) = a^m * a^n`

2. Law of Exponents: Base raised to the power of a product (or quotient) is equal to the base raised to the power of the numerator raised to the exponent and the base raised to the power of the denominator raised to the negative exponent.

Example:
`a^(mn)` =
`(a^m)^n or a^(m/n)` =
`root(n)(a)^m`

3. Law of Exponents: Base raised to an exponent of zero is equal to one (except for zero as the base).

Example: a^0 = 1 (except for a = 0)

Using these laws, we can simplify each expression as follows:

A)
`2^3` *
`2^2` =
`2^5` (using law 1)

B)
`5^0` = 1 (using law 3)

C)
`3^4 / 3^2 = 3^2`(using law 2)

D)
`x^5 / y^3` =
`(x/y)^5` (using law 2)