Which expression is equivalent to (x2y3)4(x3y2)2
?
Responses
x2y3
x squared y cubed
x2y8
x squared y to the 8th power
x14y16
x to the 14th power y to the 16th power
x11y11
x to the 11th power y to the 11th power
To simplify the given expression, we need to apply the exponent rules.
First, let's simplify the first part of the expression, which is (x^2y^3)^4. To raise a power to another power, we need to multiply the exponents. So, (x^2y^3)^4 becomes x^(2*4) * y^(3*4) = x^8 * y^12.
Now, let's simplify the second part of the expression, which is (x^3y^2)^2. Again, we raise the power to another power, resulting in x^(3*2) * y^(2*2) = x^6 * y^4.
Finally, to find the equivalent expression, we multiply the simplified expressions we obtained from the first and second parts:
x^8 * y^12 * x^6 * y^4 = x^(8+6) * y^(12+4) = x^14 * y^16.
Therefore, the equivalent expression is x^14 * y^16.
To simplify the given expression (x^2y^3)^4(x^3y^2)^2, follow these steps:
Step 1: Simplify (x^2y^3)^4.
- Raise the coefficients, x and y, to the power of 4 individually:
(x^2)^4 = x^8 and (y^3)^4 = y^12.
- So, (x^2y^3)^4 simplifies to x^8y^12.
Step 2: Simplify (x^3y^2)^2.
- Raise the coefficients, x and y, to the power of 2 individually:
(x^3)^2 = x^6 and (y^2)^2 = y^4.
- So, (x^3y^2)^2 simplifies to x^6y^4.
Step 3: Multiply the simplified expressions from step 1 and step 2:
x^8y^12 * x^6y^4.
Step 4: Apply the rule of exponents, which states that when multiplying variables with the same base, you add the exponents:
x^8y^12 * x^6y^4 = x^(8+6)y^(12+4) = x^14y^16.
Therefore, the expression (x^2y^3)^4(x^3y^2)^2 simplifies to x^14y^16.