Algebra

7 / (49^(1/3))

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Rewrite 49 as a power of 7

We recognize that 49 equals 7 squared. Writing it this way lets us use exponent rules to simplify.
2

Rewrite the denominator using exponents

When you raise a power to another power, you multiply the exponents. So .
3

Rewrite the full expression

Now both the numerator and denominator are powers of 7, so we can use the quotient rule for exponents.
4

Apply the quotient rule for exponents

The quotient rule says . So we subtract: .
5

Express the answer as a radical

A fractional exponent of means the cube root. Both forms are correct — and are the same thing.

Understanding this problem

Learning Insight

Fractional exponents and radicals are two ways to write the same thing. When you divide powers with the same base, you subtract exponents. Rewriting numbers as powers of a common base (like writing 49 as ) is a key strategy that unlocks simplification.

Quick Tip

Whenever you see a number like 49, 27, 32, or 125 in a problem with exponents or roots, immediately ask yourself: 'Is this a perfect power of a smaller number?' Rewriting it that way almost always makes the problem easier.

Common Mistake

Students often try to simplify by writing it as and then taking the cube root — but you cannot separate the exponent from the base that way. The exponent applies only to 49, not to the fraction .