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Popular >

simplify 11^{1/4 log_{11}(16)}

Solution

simplify

1 1^{\frac{1}{4} l o g_{11} (16)}

Solution

2

Solution steps

1 1^{\frac{1}{4} l o g_{11} (16)}

Apply exponent rule:

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

1 1^{\frac{1}{4} l o g_{11} (16)} = (1 1^{l o g_{11} (16)})^{\frac{1}{4}}

= (1 1^{l o g_{11} (16)})^{\frac{1}{4}}

Apply log rule:

a^{l o g_{a} (b)} = b

1 1^{l o g_{11} (16)} = 16

= 1 6^{\frac{1}{4}}

Factor the number:

16 = 2^{4}

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

Apply exponent rule:

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

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

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

= 2^{1}

Apply exponent rule:

a^{1} = a

= 2

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Frequently Asked Questions (FAQ)

What is 11^{1/4 log_{11}(16)} ?
The solution to 11^{1/4 log_{11}(16)} is 2