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\left(a^{1}b^{4}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(a^{1}\right)^{2}\left(b^{4}\right)^{2}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
a^{2}b^{4\times 2}
To raise a power to another power, multiply the exponents.
a^{2}b^{8}
Multiply 4 times 2.
\left(a^{1}b^{4}\right)^{2}
Use the rules of exponents to simplify the expression.
\left(a^{1}\right)^{2}\left(b^{4}\right)^{2}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
a^{2}b^{4\times 2}
To raise a power to another power, multiply the exponents.
a^{2}b^{8}
Multiply 4 times 2.