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

00:00 Simplify

00:03 According to the laws of exponents, any base (A) to the power of (M) to the power of (N)

00:07 equals the same base (A) to the power of the product of exponents (M*N)

00:11 Let's use this formula in our exercise

00:16 Let's compare terms according to the formula and simplify

00:20 Let's keep the base

00:26 Let's multiply the exponents

00:53 Let's use the same method to simplify the second base

01:17 And this is the solution to 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 $\boxed{3^8 \times 5^{15}}$ .