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Find equivalent to root(4)(81a^(4)b^(8)) ?

Find equivalent to 81a4b84 \sqrt[4]{81 a^{4} b^{8}} ?

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Simplify the product of two radical expressions having same variableright chevron icon

Full solution

Q. Find equivalent to 81a4b84 \sqrt[4]{81 a^{4} b^{8}} ?
  1. Break down into prime factors: First, let's break down the number 8181 into its prime factors.81=3481 = 3^4
  2. Express as exponential expression: Now, let's express the entire radical as an exponential expression. 81a4b84=(81a4b8)14\sqrt[4]{81a^{4}b^{8}} = (81a^{4}b^{8})^{\frac{1}{4}}
  3. Substitute and simplify: Substitute 8181 with 343^4 in the expression.\newline(34a4b8)1/4(3^4a^{4}b^{8})^{1/4}
  4. Apply power of a power rule: Apply the power of a power rule (am)n=am∗n(a^{m})^{n} = a^{m*n}.\newline34∗(1/4)a4∗(1/4)b8∗(1/4)3^{4*(1/4)}a^{4*(1/4)}b^{8*(1/4)}
  5. Simplify the exponents: Simplify the exponents. 31a1b23^1a^1b^2
  6. Write the simplified expression: Write the simplified expression. 3ab23ab^2

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