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(2y^(4))^(3)(5y^(6))^(2)=

$\left(2 y^{4}\right)^{3}\left(5 y^{6}\right)^{2}=$

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Multiplication with rational exponents

Full solution

Q.

\left(2 y^{4}\right)^{3}\left(5 y^{6}\right)^{2}=

Apply Power Rule: First, apply the power of a power rule: a^m)^n = a^{m*n}\.\(\newline\$2y^{4}\)^{\(3\)} = \(2\)^{\(3\)} * \(y^{4}\)^{\(3\)} = \(8\)y^{\(12\)},\(\newline\)\(5y^{6}\)^{\(2\)} = \(5\)^{\(2\)} * \(y^{6}\)^{\(2\)} = \(25\)y^{\(12\)},
Multiply Results: Next, multiply the results from step \(1\).\(\newline\)\(8y^{12} \times 25y^{12} = (8\times25)(y^{12}\times y^{12}),\)
Simplify Multiplication: Now, simplify the multiplication and apply the rule of exponents: \(a^m \times a^n = a^{m+n}\). \(\newline\)\((8\times25)(y^{12}\times y^{12}) = 200y^{24}\),

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