To calculate: To convert the radical expression 64x63 to rational exponent form and simplify.

Calculation: According to exponential rules, an=a1n Applying the above rule: 64x63=(64x63)12 Applying the rule again: 64x63=((64x6)13)12 According to the power rule, (am)n=amn Applying the above rule: 64x63=(64x6)(13)(12) 64x63=(64x6)(16) This can be written as 64x63=(26x6)(16) According to product rule, (ab)n=an⋅bn Applying the above rule: 64x63=(26)(16)(x6)(16) Applying the power rule: 64x63=2(6)(16)x(6)(16) 64x63=21x1 64x63=2x

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jernplate8

Answered question

2021-10-21

To calculate:
To convert the radical expression $\sqrt{\sqrt[3]{64 x^{6}}}$ to rational exponent form and simplify.

Answer & Explanation

pivonie8

Skilled2021-10-22Added 91 answers

Calculation:
According to exponential rules, $\sqrt[n]{a} = a^{\frac{1}{n}}$
Applying the above rule:
$\sqrt{\sqrt[3]{64 x^{6}}} = (\sqrt[3]{64 x^{6}})^{\frac{1}{2}}$
Applying the rule again:
$\sqrt{\sqrt[3]{64 x^{6}}} = ((64 x^{6})^{\frac{1}{3}})^{\frac{1}{2}}$
According to the power rule, ${(a^{m})}^{n} = a^{m n}$
Applying the above rule:
$\sqrt{\sqrt[3]{64 x^{6}}} = (64 x^{6})^{(\frac{1}{3}) (\frac{1}{2})}$
$\sqrt{\sqrt[3]{64 x^{6}}} = (64 x^{6})^{(\frac{1}{6})}$
This can be written as
$\sqrt{\sqrt[3]{64 x^{6}}} = (2^{6} x^{6})^{(\frac{1}{6})}$
According to product rule, ${(a b)}^{n} = a^{n} \cdot b^{n}$
Applying the above rule:
$\sqrt{\sqrt[3]{64 x^{6}}} = (2^{6})^{(\frac{1}{6})} (x^{6})^{(\frac{1}{6})}$
Applying the power rule:
$\sqrt{\sqrt[3]{64 x^{6}}} = 2^{(6) (\frac{1}{6})} x^{(6) (\frac{1}{6})}$
$\sqrt{\sqrt[3]{64 x^{6}}} = 2^{1} x^{1}$
$\sqrt{\sqrt[3]{64 x^{6}}} = 2 x$

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