What is simplify-(2^{-2})(81^{-1/2}) ?

The solution to simplify-(2^{-2})(81^{-1/2}) is -1/36

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simplify-(2^{-2})(81^{-1/2})

simplify

- (2^{- 2}) (8 1^{- \frac{1}{2}})

- \frac{1}{36}

Decimal Notation

- 0.02777 \dots

Solution steps

- (2^{- 2}) (8 1^{- \frac{1}{2}})

- (2^{- 2}) (8 1^{- \frac{1}{2}}) = - 2^{- 2} \cdot 8 1^{- \frac{1}{2}}

= - 2^{- 2} \cdot 8 1^{- \frac{1}{2}}

2^{- 2} = \frac{1}{4}

= - \frac{1}{4} \cdot 8 1^{- \frac{1}{2}}

Factor the number:

81 = 9^{2}

= - \frac{1}{4} (9^{2})^{- \frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

(9^{2})^{- \frac{1}{2}} = 9^{2 (- \frac{1}{2})}

= - \frac{1}{4} \cdot 9^{2 (- \frac{1}{2})}

2 (- \frac{1}{2}) = - 1

= - \frac{1}{4} \cdot 9^{- 1}

Apply exponent rule:

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

9^{- 1} = \frac{1}{9}

= - \frac{1}{4} \cdot \frac{1}{9}

- \frac{1}{4} \cdot \frac{1}{9} = - \frac{1}{36}

= - \frac{1}{36}

(1 + 9 x) \cdot (- 10)

b^{3 l o g_{b} (10)}

- 7 + (- 9)

243 - 32 x^{5}

What is simplify-(2^{-2})(81^{-1/2}) ?
The solution to simplify-(2^{-2})(81^{-1/2}) is -1/36