use the properties of exponents to simplify each expression.(2x0y4)3
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To simplify the expression (2x^0y^4)^3 using the properties of exponents, we can follow these steps:
Step 1: Recall that any number or variable raised to the power of zero is equal to 1. Therefore, x^0 = 1.
Step 2: Applying this property, we simplify the expression to (2 * 1 * y^4)^3.
Step 3: Simplify further by multiplying 2 and 1, which gives us (2y^4)^3.
Step 4: To raise a power to another power, we multiply the exponents. In this case, we have (2^3 * (y^4)^3).
Step 5: Evaluate the exponent of 2: 2^3 = 8.
Step 6: For the exponent of y, apply the same rule: (y^4)^3 = y^(4 * 3) = y^12.
Putting it all together, the simplified expression is 8y^12.
To simplify the expression (2x^0y^4)^3 using the properties of exponents, follow these steps:
Step 1: Identify the exponents and base within the parenthesis.
In this case, the base is (2x^0y^4) and the exponent is 3.
Step 2: Simplify the base.
The exponent of 0 on x means that x^0 equals 1, because any number raised to the power of 0 is equal to 1. Therefore, (2x^0y^4) becomes (2 * 1 * y^4).
Step 3: Simplify the base further.
Multiplying any number by 1 doesn't change its value, so (2 * 1 * y^4) simplifies to just (2y^4).
Step 4: Apply the exponent to the simplified base.
Raising (2y^4) to the power of 3 means multiplying it by itself three times, resulting in (2y^4)*(2y^4)*(2y^4) = 2^3 * (y^4)^3.
Note: When you raise a power to another power, you need to multiply the exponents.
Step 5: Simplify the exponents.
Since the exponent outside the parentheses is 3, you need to multiply the exponent 3 with each exponent inside the parentheses.
Thus, 2^3 * (y^4)^3 becomes 8 * y^(4*3) = 8y^12.
Therefore, the simplified expression for (2x^0y^4)^3 is 8y^12.