what is the expression (6x^3y^6)^2 equivalent to?
6^2 * (x^3)^2 * (y^6)^2
which is
36 x^6 y^12
Well, if we take the expression (6x^3y^6) and square it, it's like taking a fancy math selfie! So, get ready to strike a pose because we're going to multiply everything inside by itself. Brace yourself for some math magic!
When we square (6x^3y^6), we have to square the coefficient (6), square the variable with the exponent (x^3), and square the other variable with the exponent (y^6). So, let's put on our magic math hats and get started:
(6x^3y^6)^2 = 6^2 * (x^3)^2 * (y^6)^2
Now, let's simplify each term and unleash the laughter of math:
= 36 * (x^3 * x^3) * (y^6 * y^6)
Since we're multiplying, we can add the exponents:
= 36 * x^(3+3) * y^(6+6)
= 36 * x^6 * y^12
So, ta-da! The expression (6x^3y^6)^2 is equivalent to 36x^6y^12. Now that's what I call squared comedy!
To simplify the expression (6x^3y^6)^2, we can use the exponent rule that states raising a power to another power requires multiplying the exponents. Therefore:
(6x^3y^6)^2 = 6^2 * (x^3)^2 * (y^6)^2
Simplifying further:
= 36 * x^(3*2) * y^(6*2)
= 36 * x^6 * y^12
Therefore, the expression (6x^3y^6)^2 is equivalent to 36x^6y^12.
To simplify the expression (6x^3y^6)^2, you need to square each term inside the parentheses. This means multiplying the entire expression by itself.
Step 1: Square the coefficient
The coefficient is 6, so when squared, it becomes 6^2 = 36.
Step 2: Square each variable term
For x^3, when squared, you need to multiply the exponents: 3 x 2 = 6. So x^3 becomes x^6.
Similarly, for y^6, when squared, you multiply the exponents: 6 x 2 = 12. So y^6 becomes y^12.
Step 3: Combine the terms
Putting it all together, the expression becomes (6^2)(x^6)(y^12). Simplifying this further, 6^2 = 36, x^6 remains the same, and y^12 remains the same.
Therefore, (6x^3y^6)^2 is equivalent to 36x^6y^12.