I really need help with this but I'm not sure if I'm going to put it in the correct form.
The problem says to multiply and simplify by factoring. Assume that all expressions under radicals represents nonnegative numbers. Simplify your answers. Type in radical forms.
3 with the square root sign over y^13 multiplied by 3 with the square root sign root sign over 16y^14
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I still really need help with this problem
To multiply and simplify by factoring the expression 3√(y^13) multiplied by 3√(16y^14), we can follow these steps:
Step 1: Write the expression in a simplified form. Simplify the expressions under the radicals if possible.
The expression 3√(y^13) can be simplified by factoring the exponent:
3√(y^13) = 3√(y^12 * y) = 3√(y^12) * 3√(y) = y^4 * 3√(y)
Similarly, the expression 3√(16y^14) can be simplified:
3√(16y^14) = 3√(16 * y^14) = 3√(2^4 * (y^7)^2) = 2^2 * (y^7) * 3√(y^7) = 4y^7 * 3√(y^7)
Step 2: Multiply the simplified expressions together.
Multiplying the expressions obtained in step 1, we get:
(y^4 * 3√(y)) * (4y^7 * 3√(y^7)) = (y^4 * 4y^7) * (3√(y) * 3√(y^7)) = 4y^11 * (3√(y) * √(y^7))
Step 3: Simplify the result further if possible.
The expression 3√(y) * √(y^7) can be simplified by multiplying the square roots together:
3√(y) * √(y^7) = 3√(y * y^7) = 3√(y^8) = 3√(y^4 * y^4) = 3√(y^4) * 3√(y^4) = y^2 * y^2 = y^4
Step 4: Write the final answer in radical form.
The final simplified result is: 4y^11 * y^4, which can be written as 4y^15.
Therefore, the expression 3√(y^13) multiplied by 3√(16y^14) simplifies to 4y^15.