Chapter 4, Problem 1MCT

To determine

To Simplify:

The given expression.

Answer to Problem 1MCT

  $y^{31}$

Explanation of Solution

Given:

The given expression is $y^{11}\cdot y^{20}$.

Concept Used:

Exponent properties:

• Product property: $a^m\cdot a^n=a^{m+n}$
• Exponent rule: $x^n=x\cdot x\cdot x\cdots \cdot x\left(n\text{ times}\right)$

Calculation:

In order to simplify the given expression, observe that since the base of both the terms is same as y and both the terms are in multiplication, so we will use the product property of exponents. So we will add the exponents and simplify further to get

  $\begin{array}{c}{y}^{11}\cdot y^{20}=y^{11+20}\\ =y^{31}\end{array}$

Thus, the given expression simplifies to $y^{31}$.