Math Problem Statement

Which is equivalent to 7^(3/5) x 7^(1/5)?

Solution

Let’s analyze the problem:

The question asks for the equivalent of 73/5×71/57^{3/5} \times 7^{1/5}.

Step 1: Simplify using the rule of exponents

When multiplying terms with the same base, you add the exponents: 73/5×71/5=7(3/5+1/5)7^{3/5} \times 7^{1/5} = 7^{(3/5 + 1/5)}

Step 2: Add the exponents

3/5+1/5=4/53/5 + 1/5 = 4/5

Thus, the expression simplifies to: 74/57^{4/5}

Step 3: Match the options

The correct answer is C. 74/57^{4/5}.


Would you like a detailed explanation of exponent rules or have more questions? Here are some related questions to expand your understanding:

  1. What are the laws of exponents for division and power of a power?
  2. How can we simplify fractional exponents like am/na^{m/n}?
  3. What happens if we divide 73/57^{3/5} by 71/57^{1/5}?
  4. How do negative exponents affect the base of a number?
  5. What is the relationship between radical expressions and fractional exponents?

Tip:

When working with exponents, always check if the base is the same before applying rules!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponents
Simplifying Expressions

Formulas

a^m * a^n = a^(m+n)

Theorems

Law of Exponents for Multiplication

Suitable Grade Level

Grades 7-9