The expression as a product of radicals is (7^(1/2))^3 = 7^(1/2) * 7^(1/2) * 7^(1/2) .
Radical form: An expression in radical form is an expression that contains a radical symbol, which is the symbol for the square root.
A radical expression can be simplified by factoring a perfect square out of the radicand (the number under the radical symbol).
Properties of exponents:
Product rule: When multiplying powers with the same base, add the exponents.
Quotient rule: When dividing powers with the same base, subtract the exponents.
Power of a power rule:
When raising a power to another power, multiply the exponents.
Representing 7 3/4 in radical form:
To represent 7 3/4 in radical form, we can use the following steps:
Rewrite the expression as a power with a rational exponent.
7 3/4 = 7^(3/4)
Factor the radicand into a perfect square and a non-perfect square.
7^(3/4) = (7^(1/2))^3
Write the expression as a product of radicals.
(7^(1/2))^3 = 7^(1/2) * 7^(1/2) * 7^(1/2)
Therefore, 7 3/4 in radical form is 7^(1/2) * 7^(1/2) * 7^(1/2).