Solve for Q Q = cube root of 36^(2^-1)+125^(3^-1)-81^(2^-2)

$Q = \sqrt[3]{36^{2^{- 1}} + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$Q = \sqrt[3]{36^{\frac{1}{2}} + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Step 2

Simplify the expression.

Rewrite $36$ as $6^{2}$ .

$Q = \sqrt[3]{{(6^{2})}^{\frac{1}{2}} + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$Q = \sqrt[3]{6^{2 (\frac{1}{2})} + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Step 3

Cancel the common factor of $2$ .

Cancel the common factor.

$Q = \sqrt[3]{6^{2 (\frac{1}{2})} + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Rewrite the expression.

$Q = \sqrt[3]{6^{1} + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Step 4

Evaluate the exponent.

$Q = \sqrt[3]{6 + 125^{3^{- 1}} - 81^{2^{- 2}}}$

Step 5

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$Q = \sqrt[3]{6 + 125^{\frac{1}{3}} - 81^{2^{- 2}}}$

Step 6

Simplify the expression.

Rewrite $125$ as $5^{3}$ .

$Q = \sqrt[3]{6 + {(5^{3})}^{\frac{1}{3}} - 81^{2^{- 2}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$Q = \sqrt[3]{6 + 5^{3 (\frac{1}{3})} - 81^{2^{- 2}}}$

Step 7

Cancel the common factor of $3$ .

Cancel the common factor.

$Q = \sqrt[3]{6 + 5^{3 (\frac{1}{3})} - 81^{2^{- 2}}}$

Rewrite the expression.

$Q = \sqrt[3]{6 + 5^{1} - 81^{2^{- 2}}}$

Step 8

Evaluate the exponent.

$Q = \sqrt[3]{6 + 5 - 81^{2^{- 2}}}$

Step 9

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$Q = \sqrt[3]{6 + 5 - 81^{\frac{1}{2^{2}}}}$

Step 10

Simplify the expression.

Raise $2$ to the power of $2$ .

$Q = \sqrt[3]{6 + 5 - 81^{\frac{1}{4}}}$

Rewrite $81$ as $3^{4}$ .

$Q = \sqrt[3]{6 + 5 - {(3^{4})}^{\frac{1}{4}}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$Q = \sqrt[3]{6 + 5 - 3^{4 (\frac{1}{4})}}$

Step 11

Cancel the common factor of $4$ .

Cancel the common factor.

$Q = \sqrt[3]{6 + 5 - 3^{4 (\frac{1}{4})}}$

Rewrite the expression.

$Q = \sqrt[3]{6 + 5 - 3^{1}}$

Step 12

Evaluate the exponent.

$Q = \sqrt[3]{6 + 5 - 1 \cdot 3}$

Step 13

Multiply $- 1$ by $3$ .

$Q = \sqrt[3]{6 + 5 - 3}$

Step 14

Add $6$ and $5$ .

$Q = \sqrt[3]{11 - 3}$

Step 15

Subtract $3$ from $11$ .

$Q = \sqrt[3]{8}$

Step 16

Rewrite $8$ as $2^{3}$ .

$Q = \sqrt[3]{2^{3}}$

Step 17

Pull terms out from under the radical, assuming real numbers.

$Q = 2$

Solve for Q Q = cube root of 36^(2^-1)+125^(3^-1)-81^(2^-2)

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