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 = _
9 answers
(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) = _ + 1/2 (_ - _)
(-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
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
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.
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.