Simplify (3²)⁴×(5³)⁵: Complex Exponent Reduction Problem

Reduce the following equation:

$\left(3^2\right)^4\times\left(5^3\right)^5=$

Video Solution

Solution Steps

00:08 Let's start!

00:10 We'll use the formula for multiplying powers.

00:13 Any number, A, to the power of M, times the same number, A, to the power of N.

00:19 This gives us A to the power of M plus N.

00:23 We'll apply this formula in our exercise now.

00:27 First, match the numbers with the variables in the formula.

00:31 Keep the base the same and add the exponents together.

01:01 Use the same method for the second base.

01:25 And that's how we solve the question!

Step-by-Step Solution

To solve this problem, we'll employ the power of a power rule in exponents, which states that $(a^m)^n = a^{m \times n}$ .

Let's apply this rule to each part of the expression:

Step 1: Simplify $(3^2)^4$
According to the power of a power rule, this becomes $3^{2 \times 4} = 3^8$ .
Step 2: Simplify $(5^3)^5$
Similarly, apply the rule here to get $5^{3 \times 5} = 5^{15}$ .

After simplifying both parts, we multiply the results:

$3^8 \times 5^{15}$

Thus, the reduced expression is $\boxed{3^8 \times 5^{15}}$ .