What is (7^{-3/4}*7^{1/4})^{-1} ?

The solution to (7^{-3/4}*7^{1/4})^{-1} is 7^{1/2}

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simplify (7^{-3/4}*7^{1/4})^{-1}

simplify

(7^{- \frac{3}{4}} \cdot 7^{\frac{1}{4}})^{- 1}

7^{\frac{1}{2}}

Decimal Notation

2.64575 \dots

Solution steps

(7^{- \frac{3}{4}} \cdot 7^{\frac{1}{4}})^{- 1}

Apply exponent rule:

a^{- 1} = \frac{1}{a}

(7^{- \frac{3}{4}} \cdot 7^{\frac{1}{4}})^{- 1} = \frac{1}{7 ^{- \frac{3}{4}} \cdot 7 ^{\frac{1}{4}}}

= \frac{1}{7 ^{- \frac{3}{4}} \cdot 7 ^{\frac{1}{4}}}

7^{- \frac{3}{4}} \cdot 7^{\frac{1}{4}} = 7^{- \frac{3}{4} + \frac{1}{4}}

= \frac{1}{7 ^{- \frac{3}{4} + \frac{1}{4}}}

Combine the fractions

- \frac{3}{4} + \frac{1}{4} : - \frac{1}{2}

= \frac{1}{7 ^{- \frac{1}{2}}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

7^{- \frac{1}{2}} = \frac{1}{7 ^{\frac{1}{2}}}

= \frac{1}{\frac{1}{7 ^{\frac{1}{2}}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{7 ^{\frac{1}{2}}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 7^{\frac{1}{2}}

x^{2} - 6 x - 27 = 0

3 (w + 2) - w = 2 (w - 1) + 5

5 - 4 (1 - x) \leq 4

7^{2} + 3^{2}

16 x^{4} - (y - 1)^{2}

What is (7^{-3/4}*7^{1/4})^{-1} ?
The solution to (7^{-3/4}*7^{1/4})^{-1} is 7^{1/2}