High School

Express the following number in exponential form:

(iv) [tex]3125 = 5^5[/tex]

Simplify the expression:

(iv) [tex]9^3 \times 9^2[/tex]

Answer :

Sure! Let's break down the problem step-by-step:

We are asked to simplify the expression [tex]\(9^3 \times 9^2\)[/tex] into exponential form.

Step 1: Understanding Exponents

First, let's recall a basic property of exponents: when you multiply expressions with the same base, you add the exponents. This property is expressed as:

[tex]\[ a^m \times a^n = a^{m+n} \][/tex]

In this case, the base [tex]\(a\)[/tex] is 9, and we have two exponents: 3 and 2.

Step 2: Apply the Exponent Rule

Now, let's apply this rule to our expression:

[tex]\[ 9^3 \times 9^2 = 9^{3+2} \][/tex]

Step 3: Calculate the Sum of the Exponents

Add the exponents together:

[tex]\[ 3 + 2 = 5 \][/tex]

Step 4: Write the Simplified Expression

So, the expression [tex]\(9^3 \times 9^2\)[/tex] can be simplified to:

[tex]\[ 9^5 \][/tex]

Therefore, the expression in exponential form is [tex]\(9^5\)[/tex].