Evaluate 7^(1/4)*49^(-5/8)

Problem

7^(1/4)⋅49^(−5/8)

Solution

1. Rewrite the base of the second term so that both terms have a common base of 7

49=7^2

2. Substitute the new base into the expression.

7^(1/4)⋅(7^2)^(−5/8)

3. Apply the power of a power rule, which states (a^m)^n=a^(m⋅n) to the second term.

2⋅−5/8=−10/8

4. Simplify the exponent of the second term.

−10/8=−5/4

5. Apply the product rule for exponents, a^m⋅a^n=a^(m+n) by adding the exponents.

1/4+(−5/4)=−4/4

6. Simplify the resulting exponent.

−1

7. Evaluate the final expression using the negative exponent rule a^(−n)=1/(a^n)

7^(−1)=1/7

Final Answer

7^(1/4)⋅49^(−5/8)=1/7

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