Exponents Rules - Examples, Exercises and Solutions

Understanding Exponents Rules

Complete explanation with examples

Definition of Exponentiation

Exponents are a way to write the multiplication of a term by itself several times in a shortened form.

The number that is multiplied by itself is called the base, while the number of times the base is multiplied is called the exponent.

A - Exponentiation

an=aaa a^n=a\cdot a\cdot a ... (n times)

For example:

5555=54 5\cdot5\cdot5\cdot5=5^4

5 5 is the base, while 4 4 is the exponent.

In this case, the number 5 5 is multiplied by itself 4 4 times and, therefore, it is expressed as 5 5 to the fourth power or 5 5 to the power of 4 4 .

Detailed explanation

Practice Exponents Rules

Test your knowledge with 78 quizzes

Simplify the following equation:

\( 7^5\times2^3\times7^2\times2^4= \)

Examples with solutions for Exponents Rules

Step-by-step solutions included
Exercise #1

2423= \frac{2^4}{2^3}=

Step-by-Step Solution

Let's keep in mind that the numerator and denominator of the fraction have terms with the same base, therefore we use the property of powers to divide between terms with the same base:

bmbn=bmn \frac{b^m}{b^n}=b^{m-n}

We apply it in the problem:

2423=243=21 \frac{2^4}{2^3}=2^{4-3}=2^1

Remember that any number raised to the 1st power is equal to the number itself, meaning that:

b1=b b^1=b

Therefore, in the problem we obtain:

21=2 2^1=2

Therefore, the correct answer is option a.

Answer:

2 2

Video Solution
Exercise #2

9993= \frac{9^9}{9^3}=

Step-by-Step Solution

Note that in the fraction and its denominator, there are terms with the same base, so we will use the law of exponents for division between terms with the same base:

bmbn=bmn \frac{b^m}{b^n}=b^{m-n}

Let's apply it to the problem:

9993=993=96 \frac{9^9}{9^3}=9^{9-3}=9^6

Therefore, the correct answer is b.

Answer:

96 9^6

Video Solution
Exercise #3

(35)4= (3^5)^4=

Step-by-Step Solution

To solve the exercise we use the power property:(an)m=anm (a^n)^m=a^{n\cdot m}

We use the property with our exercise and solve:

(35)4=35×4=320 (3^5)^4=3^{5\times4}=3^{20}

Answer:

320 3^{20}

Video Solution
Exercise #4

(62)13= (6^2)^{13}=

Step-by-Step Solution

We use the formula:

(an)m=an×m (a^n)^m=a^{n\times m}

Therefore, we obtain:

62×13=626 6^{2\times13}=6^{26}

Answer:

626 6^{26}

Video Solution
Exercise #5

50= 5^0=

Step-by-Step Solution

We use the power property:

X0=1 X^0=1 We apply it to the problem:

50=1 5^0=1 Therefore, the correct answer is C.

Answer:

1 1

Video Solution

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