Solve for x in (3/10)^x: Complete the Exponential Expression

Question

Insert the corresponding expression:

(32×5)x= \left(\frac{3}{2\times5}\right)^x=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:04 According to the laws of exponents, a fraction raised to the power (N)
00:08 equals the numerator and denominator raised to the same power (N)
00:13 We will apply this formula to our exercise
00:18 According to the laws of exponents when a product is raised to the power (N)
00:24 it is equal to each factor in the product separately raised to the same power (N)
00:28 We will apply this formula to our exercise
00:33 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given expression.
  • Step 2: Apply the exponent rule (ab)n=anbn\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} to distribute xx to numerator and denominator.
  • Step 3: Simplify the denominator expression by distributing exponent xx to each factor.

Now, let's work through each step:
Step 1: We have the original expression (32×5)x\left(\frac{3}{2 \times 5}\right)^x.
Step 2: Apply the rule to get 3x(2×5)x\frac{3^x}{(2 \times 5)^x}.
Step 3: Expand the denominator: (2×5)x=2x×5x(2 \times 5)^x = 2^x \times 5^x. This leads us to 3x2x×5x\frac{3^x}{2^x \times 5^x}.

Therefore, the solution to the problem is 3x2x×5x \frac{3^x}{2^x \times 5^x} .

Answer

3x2x×5x \frac{3^x}{2^x\times5^x}