To calculate: To convert the radical expression 4947 to rational exponent form and simplify.

Given: 4947 Calculation: According to exponential rules, an=a1n Applying the above rule: 4947=(49)14(7)12 This can be written as: 4947=(72)14(7)12 According to the power rule, (am)n=amn Applying the above rule: 4947=7(2)(14)7(12) 4947=7(12)7(12) According to the product rule, am⋅an=am+n Applying the above rule: 4947=712+12 4947=71 4947=7.

Best solutions to - "To calculate: To convert the radical expression 4947..."

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Kaycee Roche

Answered question

2021-11-09

To calculate:
To convert the radical expression $\sqrt[4]{49} \sqrt{7}$ to rational exponent form and simplify.

Answer & Explanation

toroztatG

Skilled2021-11-10Added 98 answers

Given: $\sqrt[4]{49} \sqrt{7}$
Calculation:
According to exponential rules, $\sqrt[n]{a} = a^{\frac{1}{n}}$
Applying the above rule:
$\sqrt[4]{49} \sqrt{7} = (49)^{\frac{1}{4}} (7)^{\frac{1}{2}}$
This can be written as:
$\sqrt[4]{49} \sqrt{7} = (7^{2})^{\frac{1}{4}} (7)^{\frac{1}{2}}$
According to the power rule, ${(a^{m})}^{n} = a^{m n}$
Applying the above rule:
$\sqrt[4]{49} \sqrt{7} = 7^{(2) (\frac{1}{4})} 7^{(\frac{1}{2})}$
$\sqrt[4]{49} \sqrt{7} = 7^{(\frac{1}{2})} 7^{(\frac{1}{2})}$
According to the product rule, $a^{m} \cdot a^{n} = a^{m + n}$
Applying the above rule:
$\sqrt[4]{49} \sqrt{7} = 7^{\frac{1}{2} + \frac{1}{2}}$
$\sqrt[4]{49} \sqrt{7} = 7^{1}$
$\sqrt[4]{49} \sqrt{7} = 7$ .

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