Question

a. Using exponential notation, we can write the product$5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5$as ______ .

b, In the expression$3^4$the number 3 is called the ______ , and the number 4 is called the _____ .

Short answer

1. Using exponential notation, we can write the product$5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5$as$5^6$
2. In the expression$3^4$the number 3 is called the base, and the number 4 is called the exponent.

Step-by-step solution

. Apply the concept of Exponential Notation

If a is any real number and n is a positive integer, then the$n^{th}$power of a is$a^n=\underset{n-times}{\underbrace{a\cdot a\cdot \mathrm{.....}\cdot a}}$

The number a is called thebase, and n is called the exponent.

. Evaluate the given expression

Given$5\cdot 5\cdot 5\cdot 5\cdot 5\cdot 5$

Here 5 appears 6-times.

. Write using Exponential Notation

Since 5 appears 6-times, we can write it in exponential notation as$5^6$where 5 is the base and 6 is the exponent.

. Apply the concept of Exponential Notation

If a is any real number and n is a positive integer, then the$n^{th}$power of a is$a^n=\underset{n-times}{\underbrace{a\cdot a\cdot \mathrm{.....}\cdot a}}$

The number a is called thebase, and n is called the exponent.

. Analyze the given Exponential Notation

Given$3^4$

It means 3 appears 4-times

. Write the components of Exponential Notation

Since 3 appears 4-times, 3 is the base and 4 is the exponent.

So, in the expression$3^4$the number 3 is called the base, and the number 4 is called the exponent