1. Apply the Zero Power Rule to create an equivalent expression to (−40)^0 + 1/2 (11−32^0)
(-40)^0 + 1/2 (11 - 32^0) = _ + 1/2 (_ - _)
2. Use the Power Rule of Exponents to simplify the expression (x^6)^5
3. Complete the table. For each of the expressions, choose which exponent rule has been used to simplify.
Product Rule Quotient Rule Power Rule Negative Integer Exponent Rule Zero Power Rule
(16^3)^9 = 16^27
6^-12/9^-15 = 9^15/6^12
11^80/11^12 = 11^58
4. (5^−3)^6 x 5^17/10^−2 = _
(5^-3)^6 x 5^17/10^-2 = _ (applying power rule, quotient rule, and product rule)
1. Apply the Zero Power Rule to create an equivalent expression to (−40)^0 + 1/2 (11−32^0)
(-40)^0 + 1/2 (11 - 32^0) = _ + 1/2 (_ - _)
(-40)^0 + 1/2 (11 - 32^0) = 1 + 1/2 (11 - 1)
2. Use the Power Rule of Exponents to simplify the expression (x^6)^5
Using the Power Rule of Exponents, we can simplify the expression (x^6)^5 as x^(6*5) which equals x^30.
3. Complete the table. For each of the expressions, choose which exponent rule has been used to simplify.
Product Rule Quotient Rule Power Rule Negative Integer Exponent Rule Zero Power Rule
(16^3)^9 = 16^27
6^-12/9^-15 = 9^15/6^12
11^80/11^12 = 11^58
(16^3)^9 = 16^27 : Power Rule
6^-12/9^-15 = 9^15/6^12: Quotient Rule
11^80/11^12 = 11^58: Quotient Rule
4. (5^−3)^6 x 5^17/10^−2 = _
To simplify the expression (5^−3)^6 x 5^17/10^−2, we can apply the Power Rule, Quotient Rule, and Product Rule of exponents.
First, let's simplify (5^−3)^6. Using the Power Rule, we raise the base (5^−3) to the power of 6, which gives us 5^(−3*6) = 5^−18.
Next, let's simplify 5^17/10^−2. Using the Quotient Rule, we subtract the exponents for the same base:
5^17/10^−2 = 5^17/10^2 = 5^17/100.
Finally, using the Product Rule, we multiply the two simplified expressions:
(5^−3)^6 x 5^17/10^−2 = 5^−18 x 5^17/100.
Now, we can combine the two expressions with the same base by adding the exponents:
5^(-18 + 17)/100 = 5^(-1)/100 = 1/5 x 100.
Therefore, the simplified expression is 100/5, which is equal to 20.
1. Apply the Zero Power Rule to create an equivalent expression to (−40)^0 + 1/2 (11−32^0):
To apply the Zero Power Rule, we know that any non-zero number raised to the power of 0 is equal to 1. So, we can simplify (-40)^0 to 1. Therefore, the expression becomes 1 + 1/2 (11 - 32^0).
(-40)^0 + 1/2 (11 - 32^0) = 1 + 1/2 (11 - 1)
2. Use the Power Rule of Exponents to simplify the expression (x^6)^5:
The Power Rule states that when a power is raised to another power, you multiply the exponents. Applying the Power Rule, we have (x^6)^5 = x^(6 * 5) = x^30.
3. Complete the table. For each of the expressions, choose which exponent rule has been used to simplify:
a) (16^3)^9 = 16^27 - The Power Rule has been used to simplify this expression by multiplying the exponents.
b) 6^-12 / 9^-15 = 9^15 / 6^12 - The Quotient Rule has been used to simplify this expression by subtracting the exponents.
c) 11^80 / 11^12 = 11^58 - The Quotient Rule has been used to simplify this expression by subtracting the exponents.
4. Simplify the expression (5^−3)^6 x 5^17 / 10^−2:
First, let's simplify (5^−3)^6 by applying the Power Rule to the base 5, where we multiply the exponents. (-3 * 6 = -18).
(5^−3)^6 = 5^(-3 * 6) = 5^(-18)
Next, we simplify (5^−18) x 5^17 by adding the exponents:
(5^−18) x 5^17 = 5^(-18 + 17) = 5^(-1)
Finally, we simplify (5^-1) / 10^-2 by applying the Negative Integer Exponent Rule, which states that a negative exponent is equivalent to the reciprocal of the positive exponent:
(5^-1) / 10^-2 = 1/5^1 x 10^2 = 1/5 x 100 = 20.
Therefore, (5^−3)^6 x 5^17 / 10^−2 simplifies to 20.