Fully simplify
(y^6)^3\cdoty^-6
To simplify this expression, we multiply the exponents when raising a power to a power and apply the property of negative exponents.
First, let's deal with the exponent outside the parentheses: (y^6)^3. This means we multiply the exponent 3 by each exponent inside the parentheses, which gives us y^(6*3) = y^18.
Next, we have y^-6. Using the property of negative exponents, we move the term with a negative exponent to the denominator and change the sign of the exponent. So, y^-6 becomes 1/y^6.
Therefore, the fully simplified expression is y^18 * 1/y^6, which can be written as y^(18 - 6) = y^12.
To fully simplify the expression (y^6)^3 * y^-6, we can use the properties of exponents.
First, let's simplify (y^6)^3. Since we are raising a power to another power, we multiply the exponents:
(y^6)^3 = y^18
Next, let's simplify y^-6. A negative exponent indicates taking the reciprocal or flipping the fraction:
y^-6 = 1/y^6
Now, we can substitute these simplifications back into the original expression:
(y^6)^3 * y^-6 = y^18 * (1/y^6)
To multiply powers with the same base, we add their exponents:
y^18 * (1/y^6) = y^(18+(-6))
Simplifying the exponent:
y^(18+(-6)) = y^12
Therefore, the fully simplified expression is y^12.
To fully simplify the expression (y^6)^3 * y^-6, we can use the laws of exponents.
First, let's simplify the expression within the parentheses. According to the exponent rule for raising a power to another power, we multiply the exponents, so (y^6)^3 becomes y^(6 * 3) = y^18.
Next, we multiply the result, y^18, by y^-6. According to the exponent rule for multiplying powers with the same base, we simply add the exponents, so y^18 * y^-6 becomes y^(18 + -6) = y^12.
Therefore, the fully simplified expression for (y^6)^3 * y^-6 is y^12.